Zhang, Sibao; Jiang, Lianxia The solutions of arithmetic function equation \(k\varphi(Y) = {\varphi_2}(Y) + S(Y^8)\). (Chinese. English summary) Zbl 1488.11013 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 45, No. 2, 194-197 (2021). MSC: 11A25 11D41 PDF BibTeX XML Cite \textit{S. Zhang} and \textit{L. Jiang}, J. Jiangxi Norm. Univ., Nat. Sci. Ed. 45, No. 2, 194--197 (2021; Zbl 1488.11013) Full Text: DOI
Gao, Qian; Gao, Li; Liang, Xiaoyan Study on mixed mean value including Smarandache LCM dual-function. (Chinese. English summary) Zbl 1488.11066 J. Hubei Univ., Nat. Sci. 43, No. 4, 413-416 (2021). MSC: 11B83 PDF BibTeX XML Cite \textit{Q. Gao} et al., J. Hubei Univ., Nat. Sci. 43, No. 4, 413--416 (2021; Zbl 1488.11066)
Zhang, Sibao; Jiang, Lianxia Discussion on the positive integer solution of equation \(k\varphi (m) = S(m^t)\). (Chinese. English summary) Zbl 1488.11012 J. Henan Univ., Nat. Sci. 51, No. 3, 367-372 (2021). MSC: 11A25 11D41 PDF BibTeX XML Cite \textit{S. Zhang} and \textit{L. Jiang}, J. Henan Univ., Nat. Sci. 51, No. 3, 367--372 (2021; Zbl 1488.11012) Full Text: DOI
Liu, Li; Li, Yu A note on solutions of an equation relating to Smarandache function. (Chinese. English summary) Zbl 1488.11009 Acta Math. Sin., Chin. Ser. 64, No. 1, 151-154 (2021). MSC: 11A25 PDF BibTeX XML Cite \textit{L. Liu} and \textit{Y. Li}, Acta Math. Sin., Chin. Ser. 64, No. 1, 151--154 (2021; Zbl 1488.11009)
Li, Changji The solvability of the equation \({\varphi_3}(n) = S (n)\). (Chinese. English summary) Zbl 1474.11011 Math. Pract. Theory 50, No. 24, 179-188 (2020). MSC: 11A25 PDF BibTeX XML Cite \textit{C. Li}, Math. Pract. Theory 50, No. 24, 179--188 (2020; Zbl 1474.11011)
Sun, Chen; Li, Jianghua; Lu, Fan The hybrid mean of the pseudo Smarandache squarefree function and \(D(n)\) function. (Chinese. English summary) Zbl 1474.11165 Math. Pract. Theory 50, No. 21, 299-304 (2020). MSC: 11N37 PDF BibTeX XML Cite \textit{C. Sun} et al., Math. Pract. Theory 50, No. 21, 299--304 (2020; Zbl 1474.11165)
Gao, Qian; Gao, Li; Liang, Xiaoyan Study on mixed mean value including Smarandache LCM function and Smarandache dual-function. (Chinese. English summary) Zbl 1474.11031 J. Hubei Univ., Nat. Sci. 42, No. 5, 500-503, 510 (2020). MSC: 11A99 PDF BibTeX XML Cite \textit{Q. Gao} et al., J. Hubei Univ., Nat. Sci. 42, No. 5, 500--503, 510 (2020; Zbl 1474.11031) Full Text: DOI
Zhu, Jie; Liao, Qunying On positive integer solutions for the equation \(Z(n) = {\varphi_e}({\mathrm{SL}}(n))\). (Chinese. English summary) Zbl 1463.11015 J. Sichuan Norm. Univ., Nat. Sci. 43, No. 4, 451-457 (2020). MSC: 11A25 11B68 PDF BibTeX XML Cite \textit{J. Zhu} and \textit{Q. Liao}, J. Sichuan Norm. Univ., Nat. Sci. 43, No. 4, 451--457 (2020; Zbl 1463.11015) Full Text: DOI
Li, Xiumei; Sha, Min A proof of Sondow’s conjecture on the Smarandache function. (English) Zbl 1460.11007 Am. Math. Mon. 127, No. 10, 939-943 (2020). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Li} and \textit{M. Sha}, Am. Math. Mon. 127, No. 10, 939--943 (2020; Zbl 1460.11007) Full Text: DOI arXiv
Zhang, Sibao The lower bound estimate for Smarandache function on two sequences. (Chinese. English summary) Zbl 1463.11090 Math. Pract. Theory 50, No. 7, 273-276 (2020). MSC: 11B83 PDF BibTeX XML Cite \textit{S. Zhang}, Math. Pract. Theory 50, No. 7, 273--276 (2020; Zbl 1463.11090)
Li, Xiumei; Sha, Min Polynomial analogue of the Smarandache function. (English) Zbl 1472.11035 J. Number Theory 217, 320-339 (2020). MSC: 11A25 11T06 11T55 PDF BibTeX XML Cite \textit{X. Li} and \textit{M. Sha}, J. Number Theory 217, 320--339 (2020; Zbl 1472.11035) Full Text: DOI arXiv
Zhu, Jie; Liao, Qunying The solvability of the equation \(Z (n) = \varphi_e(\mathrm{SL}(n))\). (Chinese. English summary) Zbl 1449.11016 Adv. Math., Beijing 48, No. 5, 541-554 (2019). MSC: 11A25 PDF BibTeX XML Cite \textit{J. Zhu} and \textit{Q. Liao}, Adv. Math., Beijing 48, No. 5, 541--554 (2019; Zbl 1449.11016)
Bai, Hairong; Liao, Qunying On the solutions for several classes of equations related to the Smarandache function. (Chinese. English summary) Zbl 1438.11006 Acta Math. Sin., Chin. Ser. 62, No. 2, 247-254 (2019). MSC: 11A25 PDF BibTeX XML Cite \textit{H. Bai} and \textit{Q. Liao}, Acta Math. Sin., Chin. Ser. 62, No. 2, 247--254 (2019; Zbl 1438.11006)
Li, Qiao; Ma, Yunzhen; Li, Jianghua On the mean distribution of F. Smarandache function. (Chinese. English summary) Zbl 1424.11068 Pure Appl. Math. 34, No. 3, 294-300 (2018). MSC: 11B83 PDF BibTeX XML Cite \textit{Q. Li} et al., Pure Appl. Math. 34, No. 3, 294--300 (2018; Zbl 1424.11068) Full Text: DOI
Bai, Hairong; Liao, Qunying Some generalizations of Smarandache function. (Chinese. English summary) Zbl 1399.11069 J. Sichuan Norm. Univ., Nat. Sci. 41, No. 1, 32-38 (2018). MSC: 11B83 PDF BibTeX XML Cite \textit{H. Bai} and \textit{Q. Liao}, J. Sichuan Norm. Univ., Nat. Sci. 41, No. 1, 32--38 (2018; Zbl 1399.11069) Full Text: DOI
Das, Bhabesh; Saikia, Helen K. On the sum of unitary divisors maximum function. (English) Zbl 1425.11008 AIMS Math. 2, No. 1, 96-101 (2017). MSC: 11A25 11A41 PDF BibTeX XML Cite \textit{B. Das} and \textit{H. K. Saikia}, AIMS Math. 2, No. 1, 96--101 (2017; Zbl 1425.11008) Full Text: DOI
Ma, Yunzhen; Sun, Chen; Li, Jianghua; Niu, Xujun On the hybrid mean value of Smarandache LCM function and Smarandache function \(\bar{S} (n)\). (Chinese. English summary) Zbl 1399.11077 Pure Appl. Math. 33, No. 5, 522-529 (2017). MSC: 11B83 PDF BibTeX XML Cite \textit{Y. Ma} et al., Pure Appl. Math. 33, No. 5, 522--529 (2017; Zbl 1399.11077) Full Text: DOI
Ma, Yunzhen; Li, Jianghua On the mean value of Smarandache function. (Chinese. English summary) Zbl 1399.11076 Pure Appl. Math. 33, No. 4, 424-429 (2017). MSC: 11B83 PDF BibTeX XML Cite \textit{Y. Ma} and \textit{J. Li}, Pure Appl. Math. 33, No. 4, 424--429 (2017; Zbl 1399.11076) Full Text: DOI
Liao, Qunying; Luo, Wenli The explicit formula for the Smarandache function and solutions of related equations. (English) Zbl 1389.11067 J. Sichuan Norm. Univ., Nat. Sci. 40, No. 1, 1-10 (2017). MSC: 11B83 11B68 PDF BibTeX XML Cite \textit{Q. Liao} and \textit{W. Luo}, J. Sichuan Norm. Univ., Nat. Sci. 40, No. 1, 1--10 (2017; Zbl 1389.11067) Full Text: DOI
Wang, Xihan; Gao, Li; Li, Guorong; Xue, Yang A hybrid mean value of the Euler function \(\varphi \left( n \right)\). (Chinese. English summary) Zbl 1389.11057 Basic Sci. J. Text. Univ. 30, No. 1, 6-9 (2017). MSC: 11B68 PDF BibTeX XML Cite \textit{X. Wang} et al., Basic Sci. J. Text. Univ. 30, No. 1, 6--9 (2017; Zbl 1389.11057) Full Text: DOI
Zhang, Lixia; Zhao, Xiqing On the \(\beta\)-th hybrid mean value of the Smarandache LCM function. (Chinese. English summary) Zbl 1363.11042 J. Hubei Univ., Nat. Sci. 38, No. 4, 315-317 (2016). MSC: 11B83 PDF BibTeX XML Cite \textit{L. Zhang} and \textit{X. Zhao}, J. Hubei Univ., Nat. Sci. 38, No. 4, 315--317 (2016; Zbl 1363.11042) Full Text: DOI
Ji, Yongqiang Upper bounds and lower bounds for the pseudo-Smarandache function. (Chinese. English summary) Zbl 1363.11039 Math. Pract. Theory 46, No. 1, 275-279 (2016). MSC: 11B83 PDF BibTeX XML Cite \textit{Y. Ji}, Math. Pract. Theory 46, No. 1, 275--279 (2016; Zbl 1363.11039)
Gao, Li; Ma, Yafeng The average issue involving the Smarandache power function. (Chinese. English summary) Zbl 1363.11038 Basic Sci. J. Text. Univ. 29, No. 1, 8-10 (2016). MSC: 11B83 PDF BibTeX XML Cite \textit{L. Gao} and \textit{Y. Ma}, Basic Sci. J. Text. Univ. 29, No. 1, 8--10 (2016; Zbl 1363.11038) Full Text: DOI
Zhang, Lixia; Zhao, Xiqing; Guo, Rui; Xu, Hongxin Solvability of arithmetic function equation \(S(SL(n)) = \varphi(n)\). (Chinese. English summary) Zbl 1363.11043 Pure Appl. Math. 31, No. 5, 533-536 (2015). MSC: 11B83 11B68 PDF BibTeX XML Cite \textit{L. Zhang} et al., Pure Appl. Math. 31, No. 5, 533--536 (2015; Zbl 1363.11043) Full Text: DOI
Liu, Miaohua; Jin, Yingji A lower bound for the values of Smarandache function of Fermat numbers. (Chinese. English summary) Zbl 1349.11006 Math. Pract. Theory 45, No. 8, 283-286 (2015). MSC: 11A25 PDF BibTeX XML Cite \textit{M. Liu} and \textit{Y. Jin}, Math. Pract. Theory 45, No. 8, 283--286 (2015; Zbl 1349.11006)
Gao, Li; Ma, Yafeng An equation involving the Smarandache LCM dual function. (Chinese. English summary) Zbl 1349.11003 J. Hubei Univ., Nat. Sci. 37, No. 4, 367-371 (2015). MSC: 11A25 PDF BibTeX XML Cite \textit{L. Gao} and \textit{Y. Ma}, J. Hubei Univ., Nat. Sci. 37, No. 4, 367--371 (2015; Zbl 1349.11003) Full Text: DOI
Wang, Yang; Wang, Ting On the 4-th weighted mean value of the Smarandache double factorial dual function. (Chinese. English summary) Zbl 1340.11009 J. Inn. Mong. Norm. Univ., Nat. Sci. 44, No. 2, 149-151 (2015). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{Y. Wang} and \textit{T. Wang}, J. Inn. Mong. Norm. Univ., Nat. Sci. 44, No. 2, 149--151 (2015; Zbl 1340.11009)
Wu, Chengjing Mean value of Smarandache ceil function. (Chinese. English summary) Zbl 1340.11010 Basic Sci. J. Text. Univ. 27, No. 4, 428-430 (2014). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{C. Wu}, Basic Sci. J. Text. Univ. 27, No. 4, 428--430 (2014; Zbl 1340.11010)
Wang, Xiaohan The lower bound for Smarandache function values of Mersenne numbers. (Chinese. English summary) Zbl 1313.11020 J. Northwest Univ., Nat. Sci. Ed. 44, No. 3, 367-369 (2014). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Wang}, J. Northwest Univ., Nat. Sci. Ed. 44, No. 3, 367--369 (2014; Zbl 1313.11020)
Xu, Junbao Research on the mean value of the Smarandache ceil function. (Chinese. English summary) Zbl 1313.11116 J. Hubei Univ. Nationalities, Nat. Sci. 32, No. 1, 64-67 (2014). MSC: 11N37 PDF BibTeX XML Cite \textit{J. Xu}, J. Hubei Univ. Nationalities, Nat. Sci. 32, No. 1, 64--67 (2014; Zbl 1313.11116)
Cira, Octavian; Smarandache, Florentin Solving Diophantine equations. (English) Zbl 1312.11003 Bruxelles: EuropaNova (ISBN 978-1-59973-307-4/pbk). xv, 236 p. (2014). Reviewer: Kazimierz Szymiczek (Tychy) MSC: 11-01 11A25 11D04 11D09 11D25 11Y50 PDF BibTeX XML Cite \textit{O. Cira} and \textit{F. Smarandache}, Solving Diophantine equations. Bruxelles: EuropaNova (2014; Zbl 1312.11003) Full Text: arXiv Link
Wang, Yang; Hua, Liuqing On the mean value of a generalized power-sum Smarandache function. (Chinese. English summary) Zbl 1313.11115 J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 2, 149-151 (2014). MSC: 11N37 PDF BibTeX XML Cite \textit{Y. Wang} and \textit{L. Hua}, J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 2, 149--151 (2014; Zbl 1313.11115)
Wang, Yang On the cubic mean value and weighted mean value of the Smarandache double factorial dual function. (Chinese. English summary) Zbl 1313.11114 Math. Pract. Theory 43, No. 16, 285-289 (2013). MSC: 11N37 PDF BibTeX XML Cite \textit{Y. Wang}, Math. Pract. Theory 43, No. 16, 285--289 (2013; Zbl 1313.11114)
Wang, Yang On the quadratic mean value of the Smarandache double factorial dual function. (Chinese. English summary) Zbl 1313.11113 J. Nanyang Norm. Univ. 12, No. 9, 1-4 (2013). MSC: 11N37 PDF BibTeX XML Cite \textit{Y. Wang}, J. Nanyang Norm. Univ. 12, No. 9, 1--4 (2013; Zbl 1313.11113)
Pan, Xiaowei; Guo, Xiaoyan The value of the F. Smarandache digit sum function for some special sequences. (Chinese. English summary) Zbl 1299.11012 J. Northwest Univ., Nat. Sci. Ed. 43, No. 5, 700-702 (2013). MSC: 11A63 PDF BibTeX XML Cite \textit{X. Pan} and \textit{X. Guo}, J. Northwest Univ., Nat. Sci. Ed. 43, No. 5, 700--702 (2013; Zbl 1299.11012)
Lü, Erbing On the mean value problems of the Smarandache ceil function. (Chinese. English summary) Zbl 1299.11007 Basic Sci. J. Text. Univ. 26, No. 2, 155-157 (2013). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{E. Lü}, Basic Sci. J. Text. Univ. 26, No. 2, 155--157 (2013; Zbl 1299.11007)
Hu, Jiayuan; Qin, Wei An equation involving the dual of the Smarandache ceil function and Euler function and its solvability. (Chinese. English summary) Zbl 1299.11005 J. Northwest Univ., Nat. Sci. Ed. 43, No. 3, 364-366 (2013). MSC: 11A25 PDF BibTeX XML Cite \textit{J. Hu} and \textit{W. Qin}, J. Northwest Univ., Nat. Sci. Ed. 43, No. 3, 364--366 (2013; Zbl 1299.11005)
Chen, Bin A solvability problem of the equation involving Smarandache function. (Chinese. English summary) Zbl 1299.11004 J. Math., Wuhan Univ. 33, No. 5, 923-928 (2013). MSC: 11A25 PDF BibTeX XML Cite \textit{B. Chen}, J. Math., Wuhan Univ. 33, No. 5, 923--928 (2013; Zbl 1299.11004)
Huang, Wei; Ma, Yan Hybrid mean value estimates involving a new additive function. (Chinese. English summary) Zbl 1299.11071 J. Nanyang Norm. Univ. 12, No. 6, 8-10 (2013). MSC: 11N37 11A25 PDF BibTeX XML Cite \textit{W. Huang} and \textit{Y. Ma}, J. Nanyang Norm. Univ. 12, No. 6, 8--10 (2013; Zbl 1299.11071)
Tong, Minna A new pseudo-Smarandache function and its mean value. (Chinese. English summary) Zbl 1289.11026 Basic Sci. J. Text. Univ. 26, No. 1, 18-20 (2013). MSC: 11B83 PDF BibTeX XML Cite \textit{M. Tong}, Basic Sci. J. Text. Univ. 26, No. 1, 18--20 (2013; Zbl 1289.11026)
Che, Shun An equation involving Smarandache function \(S(n)\) and pseudo Smarandache function \(Z_1(n)\) and its positive integer solutions. (Chinese. English summary) Zbl 1289.11003 Basic Sci. J. Text. Univ. 26, No. 1, 15-17 (2013). MSC: 11A25 PDF BibTeX XML Cite \textit{S. Che}, Basic Sci. J. Text. Univ. 26, No. 1, 15--17 (2013; Zbl 1289.11003)
Wang, Yang An identity of the Smarandache double factorial dual function. (Chinese. English summary) Zbl 1274.11069 J. Nanyang Norm. Univ. 11, No. 12, 11-13 (2012). MSC: 11B83 PDF BibTeX XML Cite \textit{Y. Wang}, J. Nanyang Norm. Univ. 11, No. 12, 11--13 (2012; Zbl 1274.11069)
Bai, Yixue A special sequence and the computational problems of its digital sum in decimal expansion. (Chinese. English summary) Zbl 1274.11061 Math. Pract. Theory 42, No. 20, 229-233 (2012). MSC: 11B83 PDF BibTeX XML Cite \textit{Y. Bai}, Math. Pract. Theory 42, No. 20, 229--233 (2012; Zbl 1274.11061)
Pan, Xiaowei The non-trivial solutions of the arithmetic functional equation \(\varphi(x)=S(x^k)\). (Chinese. English summary) Zbl 1274.11013 Basic Sci. J. Text. Univ. 25, No. 3, 339-342 (2012). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Pan}, Basic Sci. J. Text. Univ. 25, No. 3, 339--342 (2012; Zbl 1274.11013)
Liu, Zhuo; Shi, Peng On the \(\beta\)-th hybrid mean value of the Smarandache function. (Chinese. English summary) Zbl 1274.11146 Basic Sci. J. Text. Univ. 25, No. 3, 335-338 (2012). MSC: 11N37 PDF BibTeX XML Cite \textit{Z. Liu} and \textit{P. Shi}, Basic Sci. J. Text. Univ. 25, No. 3, 335--338 (2012; Zbl 1274.11146)
Huang, Wei The hybrid mean value of involving the Smarandache exponent function \(e_p(n)\). (Chinese. English summary) Zbl 1274.11142 J. Baoji Univ. Arts Sci., Nat. Sci. 32, No. 3, 4-5, 27 (2012). MSC: 11N37 PDF BibTeX XML Cite \textit{W. Huang}, J. Baoji Univ. Arts Sci., Nat. Sci. 32, No. 3, 4--5, 27 (2012; Zbl 1274.11142)
Chen, Bin Positive integer solutions of an equation involving Smarandache dual function. (Chinese. English summary) Zbl 1274.11062 J. Tianjin Norm. Univ., Nat. Sci. Ed. 32, No. 3, 6-8, 17 (2012). MSC: 11B83 PDF BibTeX XML Cite \textit{B. Chen}, J. Tianjin Norm. Univ., Nat. Sci. Ed. 32, No. 3, 6--8, 17 (2012; Zbl 1274.11062)
Li, Yijun On the mean value of a new Smarandache function. (Chinese. English summary) Zbl 1265.11008 J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 3, 244-246 (2012). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{Y. Li}, J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 3, 244--246 (2012; Zbl 1265.11008)
Liu, Baoli On the F. Smarandache constructive sequence. (Chinese. English summary) Zbl 1265.11047 J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 3, 241-243 (2012). MSC: 11B83 PDF BibTeX XML Cite \textit{B. Liu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 3, 241--243 (2012; Zbl 1265.11047)
Chen, Bin A function equation related to the pseudo Smarandache function. (Chinese. English summary) Zbl 1265.11005 J. Chongqing Norm. Univ., Nat. Sci. 29, No. 2, 65-67 (2012). MSC: 11A25 PDF BibTeX XML Cite \textit{B. Chen}, J. Chongqing Norm. Univ., Nat. Sci. 29, No. 2, 65--67 (2012; Zbl 1265.11005)
Qian, Longjiang An equation involving the Smarandache function and the pseudo-Smarandache function of second kind. (Chinese. English summary) Zbl 1249.11043 Pure Appl. Math. 27, No. 5, 577-580 (2011). MSC: 11B83 PDF BibTeX XML Cite \textit{L. Qian}, Pure Appl. Math. 27, No. 5, 577--580 (2011; Zbl 1249.11043)
Li, Fenjü; Yang, Changyu A lower bound estimate problem for the Smarandache function. (Chinese. English summary) Zbl 1249.11041 J. Northwest Univ., Nat. Sci. Ed. 41, No. 3, 377-379 (2011). MSC: 11B83 PDF BibTeX XML Cite \textit{F. Li} and \textit{C. Yang}, J. Northwest Univ., Nat. Sci. Ed. 41, No. 3, 377--379 (2011; Zbl 1249.11041)
Gou, Su A new additive function and Smarandache sequences. (Chinese. English summary) Zbl 1249.11039 J. Northwest Univ., Nat. Sci. Ed. 41, No. 1, 19-21 (2011). MSC: 11B83 PDF BibTeX XML Cite \textit{S. Gou}, J. Northwest Univ., Nat. Sci. Ed. 41, No. 1, 19--21 (2011; Zbl 1249.11039)
Varbanets, P. D.; Kirbat, S. A. On the mean value of the function \(\overline{S}_k(n)\). (English. Russian original) Zbl 1244.11084 Ukr. Math. J. 63, No. 4, 516-529 (2011); translation from Ukr. Mat. Zh. 63, No. 4, 448-458 (2011). MSC: 11N37 PDF BibTeX XML Cite \textit{P. D. Varbanets} and \textit{S. A. Kirbat}, Ukr. Math. J. 63, No. 4, 516--529 (2011; Zbl 1244.11084); translation from Ukr. Mat. Zh. 63, No. 4, 448--458 (2011) Full Text: DOI
Yuan, Xia Two equations involving the F. Smarandache function. (Chinese. English summary) Zbl 1240.11022 J. Inn. Mong. Norm. Univ., Nat. Sci. 40, No. 2, 129-131 (2011). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Yuan}, J. Inn. Mong. Norm. Univ., Nat. Sci. 40, No. 2, 129--131 (2011; Zbl 1240.11022)
Yang, Mingshun On the hybrid mean value of the Smarandache function and the Smarandache LCM function. (Chinese. English summary) Zbl 1240.11119 J. Northwest Univ., Nat. Sci. Ed. 40, No. 5, 772-773, 817 (2010). MSC: 11N37 PDF BibTeX XML Cite \textit{M. Yang}, J. Northwest Univ., Nat. Sci. Ed. 40, No. 5, 772--773, 817 (2010; Zbl 1240.11119)
Zhu, Minghui On the Smarandache function and the Fermat numbers. (Chinese. English summary) Zbl 1240.11024 J. Northwest Univ., Nat. Sci. Ed. 40, No. 4, 583-585 (2010). MSC: 11A51 PDF BibTeX XML Cite \textit{M. Zhu}, J. Northwest Univ., Nat. Sci. Ed. 40, No. 4, 583--585 (2010; Zbl 1240.11024)
Chen, Guohui An equation involving the arithmetical functions \(S (d)\) and \(SL(d)\). (Chinese. English summary) Zbl 1240.11006 J. Northwest Univ., Nat. Sci. Ed. 40, No. 3, 382-384 (2010). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{G. Chen}, J. Northwest Univ., Nat. Sci. Ed. 40, No. 3, 382--384 (2010; Zbl 1240.11006)
Wang, Yang On some equations involving the Smarandache double factorial dual function. (Chinese. English summary) Zbl 1316.11009 J. Nanyang Norm. Univ. 9, No. 3, 1-3 (2010). MSC: 11A25 11B83 PDF BibTeX XML Cite \textit{Y. Wang}, J. Nanyang Norm. Univ. 9, No. 3, 1--3 (2010; Zbl 1316.11009)
Wang, Jianping A Dirichlet series involving the Smarandache summands function. (Chinese. English summary) Zbl 1240.11099 J. Shaanxi Norm. Univ., Nat. Sci. Ed. 38, No. 5, 14-17 (2010). MSC: 11M41 PDF BibTeX XML Cite \textit{J. Wang}, J. Shaanxi Norm. Univ., Nat. Sci. Ed. 38, No. 5, 14--17 (2010; Zbl 1240.11099)
Fu, Jing; Liu, Hua On a hybrid mean value of the F. Smarandache LCM function and the divisor function. (Chinese. English summary) Zbl 1240.11106 J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 560-562 (2010). MSC: 11N37 11A25 PDF BibTeX XML Cite \textit{J. Fu} and \textit{H. Liu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 560--562 (2010; Zbl 1240.11106)
Wu, Xin An equation involving the pseudo-Smarandache dual function. (Chinese. English summary) Zbl 1240.11020 J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 557-559 (2010). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Wu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 557--559 (2010; Zbl 1240.11020)
Li, Fanbei On the mean value of the Smarandache summands. (Chinese. English summary) Zbl 1240.11111 J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 555-556, 559 (2010). MSC: 11N37 PDF BibTeX XML Cite \textit{F. Li}, J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 555--556, 559 (2010; Zbl 1240.11111)
Huang, Wei; Zhao, Jiaolian Mean-value estimate for two Smarandache hybrid functions. (Chinese. English summary) Zbl 1240.11109 Pure Appl. Math. 26, No. 6, 890-894 (2010). MSC: 11N37 PDF BibTeX XML Cite \textit{W. Huang} and \textit{J. Zhao}, Pure Appl. Math. 26, No. 6, 890--894 (2010; Zbl 1240.11109)
Li, Caijuan An equation involving two Smarandache functions and its positive integer solutions. (Chinese. English summary) Zbl 1240.11013 J. Nat. Sci. Heilongjiang Univ. 27, No. 4, 446-448, 454 (2010). MSC: 11A25 PDF BibTeX XML Cite \textit{C. Li}, J. Nat. Sci. Heilongjiang Univ. 27, No. 4, 446--448, 454 (2010; Zbl 1240.11013)
Yang, Chang’en An equation concerning the Smarandache function. (Chinese. English summary) Zbl 1240.11021 Basic Sci. J. Text. Univ. 23, No. 2, 188-190 (2010). MSC: 11A25 PDF BibTeX XML Cite \textit{C. Yang}, Basic Sci. J. Text. Univ. 23, No. 2, 188--190 (2010; Zbl 1240.11021)
Zhu, Minhui On the hybrid mean value involving the F. Smarandache simple function and the Dirichlet divisor function. (Chinese. English summary) Zbl 1240.11121 J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 5, 441-443 (2010). MSC: 11N37 PDF BibTeX XML Cite \textit{M. Zhu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 5, 441--443 (2010; Zbl 1240.11121)
Wen, Tianding A lower bound estimate for the Smarandache function. (Chinese. English summary) Zbl 1224.11004 Pure Appl. Math. 26, No. 3, 413-416 (2010). MSC: 11A25 PDF BibTeX XML Cite \textit{T. Wen}, Pure Appl. Math. 26, No. 3, 413--416 (2010; Zbl 1224.11004)
Yang, Chang’en Two equations concerning the Smarandache function. (Chinese. English summary) Zbl 1224.11042 Pure Appl. Math. 26, No. 3, 387-390, 399 (2010). MSC: 11B83 PDF BibTeX XML Cite \textit{C. Yang}, Pure Appl. Math. 26, No. 3, 387--390, 399 (2010; Zbl 1224.11042)
Majumdar, A. A. K. Wandering in the world of Smarandache numbers. (English) Zbl 1223.11001 Ann Arbor, MI: ProQuest Information & Learning (ISBN 978-1-312599-74-7/pbk). 215 p. (2010). Reviewer: József Sándor (Cluj-Napoca) MSC: 11-01 11A25 11B83 PDF BibTeX XML Cite \textit{A. A. K. Majumdar}, Wandering in the world of Smarandache numbers. Ann Arbor, MI: ProQuest Information \& Learning (2010; Zbl 1223.11001)
Zhang, Jin An equation involving the pseudo Smarandache function and its dual function. (Chinese. English summary) Zbl 1224.11043 Pure Appl. Math. 25, No. 4, 786-788 (2009). MSC: 11B83 PDF BibTeX XML Cite \textit{J. Zhang}, Pure Appl. Math. 25, No. 4, 786--788 (2009; Zbl 1224.11043)
Wu, Zhaoxia; Wu, Nan A congruence equation involving the Smarandache function. (Chinese. English summary) Zbl 1212.11010 J. Northwest Univ., Nat. Sci. Ed. 39, No. 4, 549-551 (2009). MSC: 11A25 11A07 PDF BibTeX XML Cite \textit{Z. Wu} and \textit{N. Wu}, J. Northwest Univ., Nat. Sci. Ed. 39, No. 4, 549--551 (2009; Zbl 1212.11010)
Ge, Jian An equation involving the functions \(Z (n)\) and \(D (n)\) and its all positive integer solutions. (Chinese. English summary) Zbl 1212.11031 Pure Appl. Math. 25, No. 3, 622-624 (2009). MSC: 11B83 PDF BibTeX XML Cite \textit{J. Ge}, Pure Appl. Math. 25, No. 3, 622--624 (2009; Zbl 1212.11031)
Zhang, Xiaobeng; Tian, Qing Equations on the Smarandache-type multiplicative function. (Chinese. English summary) Zbl 1212.11038 Pure Appl. Math. 25, No. 3, 478-480 (2009). MSC: 11B83 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{Q. Tian}, Pure Appl. Math. 25, No. 3, 478--480 (2009; Zbl 1212.11038)
Zhu, Minhui An equation involving the Euler function and the Smarandache ceil function of order \(k\) and its positive integer solutions. (Chinese. English summary) Zbl 1199.11037 Pure Appl. Math. 25, No. 2, 414-416 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{M. Zhu}, Pure Appl. Math. 25, No. 2, 414--416 (2009; Zbl 1199.11037)
Zhao, Yuane On a congruence equation of the Smarandache function. (Chinese. English summary) Zbl 1199.11003 Pure Appl. Math. 25, No. 1, 80-82 (2009). MSC: 11A07 PDF BibTeX XML Cite \textit{Y. Zhao}, Pure Appl. Math. 25, No. 1, 80--82 (2009; Zbl 1199.11003)
He, Yanfeng; Tian, Qing A hybrid mean value formula involving the Smarandache function. (Chinese. English summary) Zbl 1199.11121 Pure Appl. Math. 25, No. 1, 129-132 (2009). MSC: 11N37 PDF BibTeX XML Cite \textit{Y. He} and \textit{Q. Tian}, Pure Appl. Math. 25, No. 1, 129--132 (2009; Zbl 1199.11121)
Li, Xiaoyan The mean value of the \(k\)-th Smarandache dual function. (English) Zbl 1226.11101 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 128-132 (2009). Reviewer: Olaf Ninnemann (Berlin) MSC: 11N37 11A25 PDF BibTeX XML Cite \textit{X. Li}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 128--132 (2009; Zbl 1226.11101)
Shang, Songye; Chen, Guohui A new Smarandache multiplicative function and its mean value formula. (English) Zbl 1226.11011 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 123-127 (2009). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{S. Shang} and \textit{G. Chen}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 123--127 (2009; Zbl 1226.11011)
Liu, Yanyan An equation involving the Smarandache power function. (English) Zbl 1226.11009 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 120-122 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{Y. Liu}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 120--122 (2009; Zbl 1226.11009)
Wang, Yang On the quadratic mean value of the Smarandache dual function \(S^{**}(n)\). (English) Zbl 1196.11133 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 109-115 (2009). MSC: 11N37 11A25 PDF BibTeX XML Cite \textit{Y. Wang}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 109--115 (2009; Zbl 1196.11133)
Yuan, Xia An equation involving the Smarandache dual function and Smarandache ceil function. (English) Zbl 1226.11012 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 106-108 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{X. Yuan}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 106--108 (2009; Zbl 1226.11012)
Fu, Ruiqin; Yang, Hai An equation involving the Lucas numbers and Smarandache primitive function. (English) Zbl 1204.11011 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 90-97 (2009). MSC: 11A25 11B39 PDF BibTeX XML Cite \textit{R. Fu} and \textit{H. Yang}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 90--97 (2009; Zbl 1204.11011)
Majumdar, A. A. K. On the dual functions \(Z_*(n)\) and \(S_*(n)\). (English) Zbl 1226.11010 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 74-77 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{A. A. K. Majumdar}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 74--77 (2009; Zbl 1226.11010)
Gunarto, H.; Majumdar, A. A. K. On numerical values of \(Z(n)\). (English) Zbl 1219.11186 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 34-57 (2009). MSC: 11Y70 11A25 11-04 PDF BibTeX XML Cite \textit{H. Gunarto} and \textit{A. A. K. Majumdar}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 34--57 (2009; Zbl 1219.11186)
Li, Fanbei; Wang, Yuguang An equation involving the Euler function and the Smarandache \(m\)-th power residues function. (English) Zbl 1219.11005 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 31-33 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{F. Li} and \textit{Y. Wang}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 31--33 (2009; Zbl 1219.11005)
Wang, Chunping; Zhao, Yanlin On an equation involving the Smarandache function and the Dirichlet divisor function. (English) Zbl 1219.11007 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 27-30 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{C. Wang} and \textit{Y. Zhao}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 27--30 (2009; Zbl 1219.11007)
Majumdar, A. A. K. \(S\)-perfect and completely \(S\)-perfect numbers. (English) Zbl 1219.11006 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 12-20 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{A. A. K. Majumdar}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 12--20 (2009; Zbl 1219.11006)
Wang, Jianping An equation related to the Smarandache power function. (English) Zbl 1219.11008 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 1-4 (2009). MSC: 11A25 PDF BibTeX XML Cite \textit{J. Wang}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 1--4 (2009; Zbl 1219.11008)
Marques, Diego A geometric proof to Cantor’s theorem and an irrationality measure for some Cantor’s series. (English) Zbl 1212.11072 Ann. Math. Inform. 36, 117-121 (2009). MSC: 11J72 11J82 PDF BibTeX XML Cite \textit{D. Marques}, Ann. Math. Inform. 36, 117--121 (2008; Zbl 1212.11072) Full Text: arXiv EuDML
Feng, Qiang; Guo, Jinbao; Wang, Rongbo On the mean values of the \(m\)-th power part and Smarandache ceil function. (Chinese. English summary) Zbl 1199.11117 J. Northwest Norm. Univ., Nat. Sci. 44, No. 3, 12-16 (2008). MSC: 11N37 11A25 PDF BibTeX XML Cite \textit{Q. Feng} et al., J. Northwest Norm. Univ., Nat. Sci. 44, No. 3, 12--16 (2008; Zbl 1199.11117)
Li, Fanbei A functional equation related to the Smarandache function and its positive integer solutions. (Chinese. English summary) Zbl 1199.11012 J. Northwest Univ., Nat. Sci. Ed. 38, No. 6, 892-894 (2008). MSC: 11A25 PDF BibTeX XML Cite \textit{F. Li}, J. Northwest Univ., Nat. Sci. Ed. 38, No. 6, 892--894 (2008; Zbl 1199.11012)
Zhang, Wenpeng On two problems of the Smarandache function. (Chinese. English summary) Zbl 1199.11033 J. Northwest Univ., Nat. Sci. Ed. 38, No. 2, 173-176 (2008). MSC: 11A25 PDF BibTeX XML Cite \textit{W. Zhang}, J. Northwest Univ., Nat. Sci. Ed. 38, No. 2, 173--176 (2008; Zbl 1199.11033)
He, Yanfeng One hybrid mean value formula involving two Smarandache functions. (English) Zbl 1199.11119 J. Nat. Sci. Heilongjiang Univ. 25, No. 4, 477-479 (2008). MSC: 11N37 PDF BibTeX XML Cite \textit{Y. He}, J. Nat. Sci. Heilongjiang Univ. 25, No. 4, 477--479 (2008; Zbl 1199.11119)
Fan, Xuhui On the pseudo-Smarandache-squarefree function and Smarandache function. (English) Zbl 1199.11008 Sci. Magna 4, No. 4, 7-11 (2008). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{X. Fan}, Sci. Magna 4, No. 4, 7--11 (2008; Zbl 1199.11008)
Zhang, Lulu; Lü, Meimei; Zhai, Wenguang On the Smarandache ceil function and the Dirichlet divisor function. (English) Zbl 1199.11126 Sci. Magna 4, No. 4, 55-57 (2008). MSC: 11N37 PDF BibTeX XML Cite \textit{L. Zhang} et al., Sci. Magna 4, No. 4, 55--57 (2008; Zbl 1199.11126)
Majumdar, A. A. K. A note on the near pseudo Smarandache function. (English) Zbl 1199.11020 Sci. Magna 4, No. 4, 104-111 (2008). MSC: 11A25 PDF BibTeX XML Cite \textit{A. A. K. Majumdar}, Sci. Magna 4, No. 4, 104--111 (2008; Zbl 1199.11020)
Zhu, Minhui An equation involving the Smarandache function and its positive integer solutions. (English) Zbl 1199.11036 Sci. Magna 4, No. 4, 1-3 (2008). MSC: 11A25 PDF BibTeX XML Cite \textit{M. Zhu}, Sci. Magna 4, No. 4, 1--3 (2008; Zbl 1199.11036)
Majumdar, A. A. K. On some pseudo Smarandache function related triangles. (English) Zbl 1199.51012 Sci. Magna 4, No. 3, 95-105 (2008). MSC: 51M04 PDF BibTeX XML Cite \textit{A. A. K. Majumdar}, Sci. Magna 4, No. 3, 95--105 (2008; Zbl 1199.51012)
Cai, Lixiang On an equation of the Smarandache function. (English) Zbl 1199.11005 Sci. Magna 4, No. 3, 71-73 (2008). MSC: 11A25 PDF BibTeX XML Cite \textit{L. Cai}, Sci. Magna 4, No. 3, 71--73 (2008; Zbl 1199.11005)