Lee, Kwangchul; Seo, Gyeong-Sig Some properties of restricted divisor functions. II. (English) Zbl 1439.11006 Proc. Jangjeon Math. Soc. 22, No. 2, 349-355 (2019). MSC: 11A05 11A25 PDF BibTeX XML Cite \textit{K. Lee} and \textit{G.-S. Seo}, Proc. Jangjeon Math. Soc. 22, No. 2, 349--355 (2019; Zbl 1439.11006) Full Text: DOI
Klyve, Dominic; Piddle, Melissa; Temple, Kathryn E. Estimating the density of the abundant numbers. (English) Zbl 1452.11008 Integers 19, Paper A16, 21 p. (2019). Reviewer: Gennady Bachman (Las Vegas) MSC: 11A25 11N60 PDF BibTeX XML Cite \textit{D. Klyve} et al., Integers 19, Paper A16, 21 p. (2019; Zbl 1452.11008) Full Text: Link
Amato, Gianluca; Hasler, Maximilian F.; Melfi, Giuseppe; Parton, Maurizio Primitive abundant and weird numbers with many prime factors. (English) Zbl 1437.11167 J. Number Theory 201, 436-459 (2019). MSC: 11Y55 11N25 11A25 PDF BibTeX XML Cite \textit{G. Amato} et al., J. Number Theory 201, 436--459 (2019; Zbl 1437.11167) Full Text: DOI
Bergelson, Vitaly; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz; Richter, Florian K. A generalization of Kátai’s orthogonality criterion with applications. (English) Zbl 1439.11167 Discrete Contin. Dyn. Syst. 39, No. 5, 2581-2612 (2019). MSC: 11J71 11K06 11N25 37A99 PDF BibTeX XML Cite \textit{V. Bergelson} et al., Discrete Contin. Dyn. Syst. 39, No. 5, 2581--2612 (2019; Zbl 1439.11167) Full Text: DOI
Lichtman, Jared Duker The reciprocal sum of primitive nondeficient numbers. (English) Zbl 1444.11014 J. Number Theory 191, 104-118 (2018). MSC: 11A25 PDF BibTeX XML Cite \textit{J. D. Lichtman}, J. Number Theory 191, 104--118 (2018; Zbl 1444.11014) Full Text: DOI
Amato, Gianluca; Hasler, Maximilian; Melfi, Giuseppe; Parton, Maurizio Primitive weird numbers having more than three distinct prime factors. (English) Zbl 1410.11005 Riv. Mat. Univ. Parma (N.S.) 7, No. 1, 153-163 (2016). MSC: 11A25 PDF BibTeX XML Cite \textit{G. Amato} et al., Riv. Mat. Univ. Parma (N.S.) 7, No. 1, 153--163 (2016; Zbl 1410.11005) Full Text: arXiv
Yadav, Shikha; Yadav, Surendra Multiplicatively perfect and related numbers. (English) Zbl 1418.11013 J. Rajasthan Acad. Phys. Sci. 15, No. 4, 345-351 (2016). MSC: 11A25 PDF BibTeX XML Cite \textit{S. Yadav} and \textit{S. Yadav}, J. Rajasthan Acad. Phys. Sci. 15, No. 4, 345--351 (2016; Zbl 1418.11013)
Melfi, Giuseppe On the conditional infiniteness of primitive weird numbers. (English) Zbl 1364.11011 J. Number Theory 147, 508-514 (2015). Reviewer: Mehdi Hassani (Zanjan) MSC: 11A25 11B83 PDF BibTeX XML Cite \textit{G. Melfi}, J. Number Theory 147, 508--514 (2015; Zbl 1364.11011) Full Text: DOI
Nicolas, Jean-Louis; Sondow, Jonathan Ramanujan, Robin, highly composite numbers, and the Riemann hypothesis. (English) Zbl 1310.01012 Alladi, Krishnaswami (ed.) et al., Ramanujan 125. International conference to commemorate the 125th anniversary of Ramanujan’s birth, University of Florida, Gainesville, FL, USA, November 5–7, 2012. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1078-0/pbk). Contemporary Mathematics 627, 145-156 (2014). Reviewer: Girish Kumar Ramaiah (Bangalore) MSC: 01A60 11M26 11A25 PDF BibTeX XML Cite \textit{J.-L. Nicolas} and \textit{J. Sondow}, Contemp. Math. 627, 145--156 (2014; Zbl 1310.01012) Full Text: arXiv
Dittmer, Samuel J. Spoof odd perfect numbers. (English) Zbl 1370.11005 Math. Comput. 83, No. 289, 2575-2582 (2014). MSC: 11A25 11A05 11A67 11D72 11N80 PDF BibTeX XML Cite \textit{S. J. Dittmer}, Math. Comput. 83, No. 289, 2575--2582 (2014; Zbl 1370.11005) Full Text: DOI
Jennings, Emily; Pollack, Paul; Thompson, Lola Variations on a theorem of Davenport concerning abundant numbers. (English) Zbl 1295.11107 Bull. Aust. Math. Soc. 89, No. 3, 437-450 (2014). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N60 11A25 11N37 PDF BibTeX XML Cite \textit{E. Jennings} et al., Bull. Aust. Math. Soc. 89, No. 3, 437--450 (2014; Zbl 1295.11107) Full Text: DOI arXiv
Nazardonyavi, Sadegh; Yakubovich, Semyon Extremely abundant numbers and the Riemann hypothesis. (English) Zbl 1342.11009 J. Integer Seq. 17, No. 2, Article 14.2.8, 23 p. (2014). MSC: 11A25 11M26 PDF BibTeX XML Cite \textit{S. Nazardonyavi} and \textit{S. Yakubovich}, J. Integer Seq. 17, No. 2, Article 14.2.8, 23 p. (2014; Zbl 1342.11009) Full Text: EMIS arXiv Backlinks: MO
Kobayashi, Mitsuo A new series for the density of abundant numbers. (English) Zbl 1288.11094 Int. J. Number Theory 10, No. 1, 73-84 (2014). Reviewer: Eira J. Scourfield (Egham) MSC: 11N60 11A25 PDF BibTeX XML Cite \textit{M. Kobayashi}, Int. J. Number Theory 10, No. 1, 73--84 (2014; Zbl 1288.11094) Full Text: DOI
Li, Yan; Ma, Lianrong; Zhang, Junhua Odd solutions of \(\sigma(n)-2n=2\) have at least six distinct prime factors. (English) Zbl 1286.11006 Publ. Math. 82, No. 2, 255-266 (2013). Reviewer: Guram Gogishvili (Tbilisi) MSC: 11A25 PDF BibTeX XML Cite \textit{Y. Li} et al., Publ. Math. 82, No. 2, 255--266 (2013; Zbl 1286.11006) Full Text: DOI
Shukla, D. P.; Yadav, Shikha Composition of arithmetical functions with generalization of perfect and related numbers. (English) Zbl 1311.11009 Commentat. Math. 52, No. 2, 153-170 (2012). Reviewer: Krassimir Atanassov (Sofia) MSC: 11A25 PDF BibTeX XML Cite \textit{D. P. Shukla} and \textit{S. Yadav}, Commentat. Math. 52, No. 2, 153--170 (2012; Zbl 1311.11009)
Pollack, Paul Long gaps between deficient numbers. (English) Zbl 1211.11006 Acta Arith. 146, No. 1, 33-42 (2011). Reviewer: Jürgen Spilker (Freiburg i. Br.) MSC: 11A25 11N60 PDF BibTeX XML Cite \textit{P. Pollack}, Acta Arith. 146, No. 1, 33--42 (2011; Zbl 1211.11006) Full Text: DOI
Guillaumin, Jean-Yves The doctrine of perfect number in a medieval gloss on Martianus Capella. (La doctrine du nombre parfait dans une glose médiévale sur Martianus Capella.) (French. English summary) Zbl 1259.01003 Laks, André (ed.) et al., Philosophie et mathématiques. Villeneuve d’Ascq: Presses Universitaires du Septentrion (ISBN 978-2-7574-0179-8/pbk). Philosophie Antique 10, 167-184 (2010). Reviewer: R. W. van der Waall (Huizen) MSC: 01A35 01A20 01A40 01A45 PDF BibTeX XML Cite \textit{J.-Y. Guillaumin}, in: Philosophie et mathématiques. Villeneuve d'Ascq: Presses Universitaires du Septentrion. 167--184 (2010; Zbl 1259.01003)
Briggs, Keith Abundant numbers and the Riemann hypothesis. (English) Zbl 1149.11041 Exp. Math. 15, No. 2, 251-256 (2006). Reviewer: Roger Heath-Brown (Oxford) MSC: 11M26 11N64 11Y55 PDF BibTeX XML Cite \textit{K. Briggs}, Exp. Math. 15, No. 2, 251--256 (2006; Zbl 1149.11041) Full Text: DOI Euclid EuDML
Nicolas, Jean-Louis Some open questions. (English) Zbl 1159.11302 Ramanujan J. 9, No. 1-2, 251-264 (2005). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{J.-L. Nicolas}, Ramanujan J. 9, No. 1--2, 251--264 (2005; Zbl 1159.11302) Full Text: DOI
Cohen, Graeme L.; Sorli, Ronald M. On the number of distinct prime factors of an odd perfect number. (English) Zbl 1116.11301 J. Discrete Algorithms 1, No. 1, 21-35 (2003). MSC: 11A25 PDF BibTeX XML Cite \textit{G. L. Cohen} and \textit{R. M. Sorli}, J. Discrete Algorithms 1, No. 1, 21--35 (2003; Zbl 1116.11301) Full Text: DOI
Deléglise, Marc Bounds for the density of abundant integers. (English) Zbl 0923.11127 Exp. Math. 7, No. 2, 137-143 (1998). Reviewer: Alberto Perelli (Genova) MSC: 11N25 11A25 PDF BibTeX XML Cite \textit{M. Deléglise}, Exp. Math. 7, No. 2, 137--143 (1998; Zbl 0923.11127) Full Text: DOI EMIS EuDML
Avidon, Michael R. On the distribution of primitive abundant numbers. (English) Zbl 0863.11002 Acta Arith. 77, No. 2, 195-205 (1996). Reviewer: M.R.Avidon (Atlanta, GA) MSC: 11A25 PDF BibTeX XML Full Text: DOI EuDML
Friedman, Charles N. Sums of divisors and Egyptian fractions. (English) Zbl 0781.11015 J. Number Theory 44, No. 3, 328-339 (1993). Reviewer: T.Tonkov (Sofia) MSC: 11D68 11A25 PDF BibTeX XML Cite \textit{C. N. Friedman}, J. Number Theory 44, No. 3, 328--339 (1993; Zbl 0781.11015) Full Text: DOI
Kierstead, Friend H. jun. Letter to the editor: Odd abundant numbers. (English) Zbl 0850.11002 J. Recreational Math. 23, No. 3, 210-211 (1991). MSC: 11A25 11-04 PDF BibTeX XML Cite \textit{F. H. Kierstead jun.}, J. Recreat. Math. 23, No. 3, 210--211 (1991; Zbl 0850.11002)
Siva Rama Prasad, V.; Reddy, D. Ram On primitive unitary abundant numbers. (English) Zbl 0691.10001 Indian J. Pure Appl. Math. 21, No. 1, 40-44 (1990). Reviewer: P.Hagis MSC: 11A25 PDF BibTeX XML Cite \textit{V. Siva Rama Prasad} and \textit{D. R. Reddy}, Indian J. Pure Appl. Math. 21, No. 1, 40--44 (1990; Zbl 0691.10001)
Prasad, V. Siva Rama; Reddy, D. Ram On unitary abundant numbers. (English) Zbl 0854.11003 Math. Stud. 52(1984), No. 1-4, 141-144 (1990). MSC: 11A25 PDF BibTeX XML Cite \textit{V. S. R. Prasad} and \textit{D. R. Reddy}, Math. Stud. 52, No. 1--4, 141--144 (1990; Zbl 0854.11003)
Le Van, Marijo Integer-perfect numbers. (English) Zbl 0636.10005 J. Nat. Sci. Math. 27, No. 2, 33-50 (1987). Reviewer: R.M.Najar MSC: 11A25 PDF BibTeX XML Cite \textit{M. Le Van}, J. Nat. Sci. Math. 27, No. 2, 33--50 (1987; Zbl 0636.10005)
Laatsch, Richard Measuring the abundancy of integers. (English) Zbl 0601.10003 Math. Mag. 59, 84-92 (1986). Reviewer: R. M. Najar (Fresno) MSC: 11A25 PDF BibTeX XML Cite \textit{R. Laatsch}, Math. Mag. 59, 84--92 (1986; Zbl 0601.10003) Full Text: DOI
Ivić, Aleksandar The distribution of primitive abundant numbers. (English) Zbl 0544.10004 Stud. Sci. Math. Hung. 20, 183-187 (1985). MSC: 11A25 11N37 PDF BibTeX XML Cite \textit{A. Ivić}, Stud. Sci. Math. Hung. 20, 183--187 (1985; Zbl 0544.10004)
Cohen, Graeme L. Primitive \(\alpha\)-abundant numbers. (English) Zbl 0551.10005 Math. Comput. 43, 263-270 (1984). Reviewer: P.Hagis MSC: 11A25 PDF BibTeX XML Cite \textit{G. L. Cohen}, Math. Comput. 43, 263--270 (1984; Zbl 0551.10005) Full Text: DOI
Wall, Charles R. A Fibonacci-like sequence of abundant numbers. (English) Zbl 0549.10006 Fibonacci Q. 22, 349 (1984). Reviewer: R.M.Najar MSC: 11B37 11A25 PDF BibTeX XML Cite \textit{C. R. Wall}, Fibonacci Q. 22, 349 (1984; Zbl 0549.10006)
Cohen, Graeme L. On primitive abundant numbers. (English) Zbl 0505.10004 J. Aust. Math. Soc., Ser. A 34, 123-137 (1983). MSC: 11A25 PDF BibTeX XML Cite \textit{G. L. Cohen}, J. Aust. Math. Soc., Ser. A 34, 123--137 (1983; Zbl 0505.10004)
Cohen, Graeme L. Generalised quasiperfect numbers. (English) Zbl 0494.10003 Thesis, Univ. New South Wales (1982), abstracted in Bull. Aust. Math. Soc. 27, 153-155 (1983). MSC: 11A25 PDF BibTeX XML
Kendall, David G. The scale of perfection. (English) Zbl 0481.01002 Essays in statistical science, Pap. in Honour of P.A.P. Moran, J. Appl. Probab., Spec. Vol. 19A, 125-138 (1982). MSC: 01A05 11A25 11-03 11B39 03A05 PDF BibTeX XML
Erdős, Paul; Nicolas, Jean-Louis Large values of a function related to the product of consecutive integers. (Grandes valeurs d’une fonction liée au produit d’entiers consecutifs.) (French) Zbl 0488.10045 Ann. Fac. Sci. Toulouse, V. Ser., Math. 3, 173-199 (1981). Reviewer: S.W..Graham MSC: 11N37 11N05 PDF BibTeX XML Cite \textit{P. Erdős} and \textit{J.-L. Nicolas}, Ann. Fac. Sci. Toulouse, Math. (5) 3, 173--199 (1981; Zbl 0488.10045) Full Text: DOI Numdam EuDML
Erdős, Paul; Babu, Gutti Jogesh; Ramachandra, K. An asymptotic formula in additive number theory. II. (English) Zbl 0438.10036 J. Indian Math. Soc., New Ser. 41, 281-291 (1977). MSC: 11P32 11N37 11N35 PDF BibTeX XML Cite \textit{P. Erdős} et al., J. Indian Math. Soc., New Ser. 41, 281--291 (1977; Zbl 0438.10036)
Erdős, Paul On the distribution of numbers of the form \(\sigma(n)/n\) and on some related questions. (English) Zbl 0291.10040 Pac. J. Math. 52, 59-65 (1974). Reviewer: S.M.Kerawala MSC: 11N60 11N37 PDF BibTeX XML Cite \textit{P. Erdős}, Pac. J. Math. 52, 59--65 (1974; Zbl 0291.10040) Full Text: DOI Euclid
Salié, Hans Über die Dichte abundanter Zahlen. (German) Zbl 0066.03005 Math. Nachr. 14, 39-46 (1955). Reviewer: F. A. Behrend MSC: 11A25 PDF BibTeX XML Cite \textit{H. Salié}, Math. Nachr. 14, 39--46 (1955; Zbl 0066.03005) Full Text: DOI
Behrend, Felix Über numeri abundantes. II. (German) Zbl 0006.39601 Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl. 1933, No. 6, 280-293 (1933). Reviewer: A. Walfisz (Radość, Poland) MSC: 11A25 PDF BibTeX XML Cite \textit{F. Behrend}, Sitzungsber. Preuß. Akad. Wiss., Phys.-Math. Kl. 1933, 280--293 (1933; Zbl 0006.39601) Full Text: EuDML
Behrend, Felix Über numeri abundantes. (German) Zbl 0005.24601 Sitzungsber. Preuß. Akad. Wiss., Phys.-Math. Kl. 1932, No. 21-23, 322-328 (1932). Reviewer: A. Walfisz (Radość, Poland) MSC: 11A25 PDF BibTeX XML Cite \textit{F. Behrend}, Sitzungsber. Preuß. Akad. Wiss., Phys.-Math. Kl. 1932, 322--328 (1932; Zbl 0005.24601) Full Text: EuDML
Gmelin, O. On perfect and amicable numbers. (Über vollkommene und befreundete Zahlen.) (German) JFM 46.0197.01 Heidelberg. Halle a. d. S.: H. John, 68 S. \(8^{\circ}\) (1917). Reviewer: v. Schrutka, Prof. (Brünn) MSC: 11A25 PDF BibTeX XML Full Text: EuDML
Dickson, L. E. Theorems and tables on the sum of the divisors of a number. (English) JFM 44.0221.02 Quart. J. 44, 264-296 (1913). Reviewer: Fueter, Prof. (Zürich) MSC: 11A25 11Y70 PDF BibTeX XML Cite \textit{L. E. Dickson}, Quart. J. 44, 264--296 (1913; JFM 44.0221.02)
Dickson, L. E. Even abundant numbers. (English) JFM 44.0221.01 Am. J. Math. 35, 423-426 (1913). Reviewer: Fueter, Prof. (Zürich) MSC: 11A25 PDF BibTeX XML Cite \textit{L. E. Dickson}, Am. J. Math. 35, 423--426 (1913; JFM 44.0221.01) Full Text: DOI
Dickson, L. E. Finiteness of the odd perfect and primitive abundant numbers with \(n\) distinct prime factors. (English) JFM 44.0220.02 Am. J. Math. 35, 413-422 (1913); Bull. Am. Math. Soc. Bull. (2) 19, 285 (1913). Reviewer: Fueter, Prof. (Zürich) MSC: 11A25 PDF BibTeX XML Cite \textit{L. E. Dickson}, Am. J. Math. 35, 413--422 (1913; JFM 44.0220.02) Full Text: DOI