Pollack, Paul; Roy, Akash Singha Powerfree sums of proper divisors. (English) Zbl 1496.11124 Colloq. Math. 168, No. 2, 287-295 (2022). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N37 11A25 11N64 PDF BibTeX XML Cite \textit{P. Pollack} and \textit{A. S. Roy}, Colloq. Math. 168, No. 2, 287--295 (2022; Zbl 1496.11124) Full Text: DOI arXiv OpenURL
Mangerel, Alexander P. Squarefree integers in arithmetic progressions to smooth moduli. (English) Zbl 1482.11125 Forum Math. Sigma 9, Paper No. e72, 47 p. (2021). Reviewer: Olivier Bordellès (Aiguilhe) MSC: 11N25 11N37 11N69 PDF BibTeX XML Cite \textit{A. P. Mangerel}, Forum Math. Sigma 9, Paper No. e72, 47 p. (2021; Zbl 1482.11125) Full Text: DOI arXiv OpenURL
Sanna, Carlo On the number of distinct exponents in the prime factorization of an integer. (English) Zbl 1439.11245 Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 27, 11 p. (2020). MSC: 11N25 11N37 11N64 PDF BibTeX XML Cite \textit{C. Sanna}, Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 27, 11 p. (2020; Zbl 1439.11245) Full Text: DOI arXiv Backlinks: MO OpenURL
Goryashin, D. V. Squarefree numbers in the sequence \([\alpha n]\). (Russian. English summary) Zbl 1430.11130 Chebyshevskiĭ Sb. 14, No. 3(47), 42-48 (2013). MSC: 11N25 PDF BibTeX XML Cite \textit{D. V. Goryashin}, Chebyshevskiĭ Sb. 14, No. 3(47), 42--48 (2013; Zbl 1430.11130) Full Text: DOI MNR OpenURL
Baker, Roger C.; Banks, William D.; Brüdern, Jörg; Shparlinski, Igor E.; Weingartner, Andreas J. Piatetski-Shapiro sequences. (English) Zbl 1327.11062 Acta Arith. 157, No. 1, 37-68 (2013). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11L07 PDF BibTeX XML Cite \textit{R. C. Baker} et al., Acta Arith. 157, No. 1, 37--68 (2013; Zbl 1327.11062) Full Text: DOI arXiv OpenURL
Tolev, D. I. On the number of pairs of positive integers \(x,y \leq H\) such that \(x^2+y^2+1\) is squarefree. (English) Zbl 1297.11118 Monatsh. Math. 165, No. 3-4, 557-567 (2012). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11L05 11N37 PDF BibTeX XML Cite \textit{D. I. Tolev}, Monatsh. Math. 165, No. 3--4, 557--567 (2012; Zbl 1297.11118) Full Text: DOI arXiv OpenURL
Luca, Florian; Pomerance, Carl On the radical of a perfect number. (English) Zbl 1230.11008 New York J. Math. 16, 23-30 (2010). Reviewer: Pentti Haukkanen (Tampere) MSC: 11A25 11N25 PDF BibTeX XML Cite \textit{F. Luca} and \textit{C. Pomerance}, New York J. Math. 16, 23--30 (2010; Zbl 1230.11008) Full Text: EuDML EMIS OpenURL
Copil, Vlad; Panaitopol, Laurenţiu Properties of a sequence generated by positive integers. (English) Zbl 1150.11034 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 50(98), No. 2, 131-137 (2007). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N60 PDF BibTeX XML Cite \textit{V. Copil} and \textit{L. Panaitopol}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 50(98), No. 2, 131--137 (2007; Zbl 1150.11034) OpenURL
Copil, Vlad; Panaitopol, Laurenţiu A sequence attached to powerful numbers. (English) Zbl 1150.11033 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 50(98), No. 3, 249-258 (2007). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11N60 PDF BibTeX XML Cite \textit{V. Copil} and \textit{L. Panaitopol}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 50(98), No. 3, 249--258 (2007; Zbl 1150.11033) OpenURL
Mincu, Gabriel; Panaitopol, Laurenţiu On some properties of squarefree and squarefull numbers. (English) Zbl 1114.11010 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 49(97), No. 1, 63-68 (2006). Reviewer: Eira J. Scourfield (Egham) MSC: 11A67 11N25 11N80 PDF BibTeX XML Cite \textit{G. Mincu} and \textit{L. Panaitopol}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 49(97), No. 1, 63--68 (2006; Zbl 1114.11010) OpenURL
De Koninck, Jean-Marie; Luca, Florian On the proximity of powerful numbers. (Sur la proximité des nombres puissants.) (French) Zbl 1048.11007 Acta Arith. 114, No. 2, 149-157 (2004). Reviewer: Aleksandar Ivić (Beograd) MSC: 11A51 11N25 11J13 PDF BibTeX XML Cite \textit{J.-M. De Koninck} and \textit{F. Luca}, Acta Arith. 114, No. 2, 149--157 (2004; Zbl 1048.11007) Full Text: DOI Link OpenURL
Granville, Andrew \(abc\) allows us to count squarefrees. (English) Zbl 0924.11018 Int. Math. Res. Not. 1998, No. 19, 991-1009 (1998). Reviewer: Ming-Chit Liu (Hongkong) MSC: 11C08 11N25 PDF BibTeX XML Cite \textit{A. Granville}, Int. Math. Res. Not. 1998, No. 19, 991--1009 (1998; Zbl 0924.11018) Full Text: DOI OpenURL
Grimmett, Geoffrey Large deviations in the random sieve. (English) Zbl 0892.11029 Math. Proc. Camb. Philos. Soc. 121, No. 3, 519-530 (1997). Reviewer: A.Hildebrand (Urbana) MSC: 11N36 11N25 11N35 PDF BibTeX XML Cite \textit{G. Grimmett}, Math. Proc. Camb. Philos. Soc. 121, No. 3, 519--530 (1997; Zbl 0892.11029) Full Text: DOI OpenURL
Friedlander, John; Iwaniec, Henryk Bombieri’s sieve. (English) Zbl 0862.11052 Berndt, Bruce C. (ed.) et al., Analytic number theory. Vol. 1. Proceedings of a conference in honor of Heini Halberstam, May 16-20, 1995, Urbana, IL, USA. Boston, MA: Birkhäuser. Prog. Math. 138, 411-430 (1996). Reviewer: M.Nair (Glasgow) MSC: 11N35 11N25 PDF BibTeX XML Cite \textit{J. Friedlander} and \textit{H. Iwaniec}, Prog. Math. 138, 411--430 (1996; Zbl 0862.11052) OpenURL
Filaseta, Michael; Trifonov, Ognian The distribution of squarefull numbers in short intervals. (English) Zbl 0819.11036 Acta Arith. 67, No. 4, 323-333 (1994). Reviewer: P.Shiu (Loughborough) MSC: 11N25 11N37 PDF BibTeX XML Cite \textit{M. Filaseta} and \textit{O. Trifonov}, Acta Arith. 67, No. 4, 323--333 (1994; Zbl 0819.11036) Full Text: DOI EuDML OpenURL
Wu, Jie \({\mathcal B}\)-free numbers in short intervals. (Nombres \({\mathcal B}\)-libres dans les petits intervalles.) (French) Zbl 0790.11067 Acta Arith. 65, No. 2, 97-116 (1993). Reviewer: G.Greaves (Cardiff) MSC: 11N25 PDF BibTeX XML Cite \textit{J. Wu}, Acta Arith. 65, No. 2, 97--116 (1993; Zbl 0790.11067) Full Text: DOI EuDML OpenURL
Filaseta, Michael On the distribution of gaps between squarefree numbers. (English) Zbl 0784.11044 Mathematika 40, No. 1, 88-101 (1993). Reviewer: A.Ivić (Beograd) MSC: 11N25 PDF BibTeX XML Cite \textit{M. Filaseta}, Mathematika 40, No. 1, 88--101 (1993; Zbl 0784.11044) Full Text: DOI OpenURL
Filaseta, Michael; Trifonov, Ognian On gaps between squarefree numbers. II. (English) Zbl 0799.11032 J. Lond. Math. Soc., II. Ser. 45, No. 2, 215-221 (1992). Reviewer: G.Greaves (Cardiff) MSC: 11N25 PDF BibTeX XML Cite \textit{M. Filaseta} and \textit{O. Trifonov}, J. Lond. Math. Soc., II. Ser. 45, No. 2, 215--221 (1992; Zbl 0799.11032) Full Text: DOI OpenURL
Filaseta, Michael; Trifonov, Ognian On gaps between squarefree numbers. (English) Zbl 0723.11044 Analytic number theory, Proc. Conf. in Honor of Paul T. Bateman, Urbana/IL (USA) 1989, Prog. Math. 85, 235-253 (1990). Reviewer: G.Kolesnik (Los Angeles) MSC: 11N25 11B05 PDF BibTeX XML OpenURL
Filaseta, Michael Short interval results for squarefree numbers. (English) Zbl 0698.10027 J. Number Theory 35, No. 2, 128-149 (1990). Reviewer: D.Wolke MSC: 11N05 11L40 PDF BibTeX XML Cite \textit{M. Filaseta}, J. Number Theory 35, No. 2, 128--149 (1990; Zbl 0698.10027) Full Text: DOI OpenURL
Popov, O. V. Quadratic residues and nonresidues in a square-free numbers sequence. (English. Russian original) Zbl 0697.10038 Mosc. Univ. Math. Bull. 44, No. 5, 77-79 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81-83 (1989). MSC: 11N69 11L40 11A15 PDF BibTeX XML Cite \textit{O. V. Popov}, Mosc. Univ. Math. Bull. 44, No. 5, 77--79 (1989; Zbl 0697.10038); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81--83 (1989) OpenURL
Popov, O. V. On quadratic residues and nonresidues in the sequence of square-free numbers. (Russian) Zbl 0684.10046 Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81-83 (1989). Reviewer: W.Narkiewicz MSC: 11N69 11L40 11A15 PDF BibTeX XML Cite \textit{O. V. Popov}, Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81--83 (1989; Zbl 0684.10046) OpenURL
Hall, R. R. The distribution of squarefree numbers. (English) Zbl 0653.10040 J. Reine Angew. Math. 394, 107-117 (1989). Reviewer: R.R.Hall MSC: 11N05 PDF BibTeX XML Cite \textit{R. R. Hall}, J. Reine Angew. Math. 394, 107--117 (1989; Zbl 0653.10040) Full Text: DOI Crelle EuDML OpenURL
Graham, S. W.; Kolesnik, G. On the difference between consecutive squarefree integers. (English) Zbl 0656.10041 Acta Arith. 49, No. 5, 435-447 (1988). Reviewer: J.Kaczorowski MSC: 11N05 11L40 PDF BibTeX XML Cite \textit{S. W. Graham} and \textit{G. Kolesnik}, Acta Arith. 49, No. 5, 435--447 (1988; Zbl 0656.10041) Full Text: DOI EuDML OpenURL
Jia, Chaohua The distribution of squarefree numbers. (Chinese) Zbl 0657.10043 Acta Sci. Nat. Univ. Pekin. 1987, No. 3, 21-27 (1987). Reviewer: P.Shiu MSC: 11N05 11L40 PDF BibTeX XML Cite \textit{C. Jia}, Acta Sci. Nat. Univ. Pekin. 1987, No. 3, 21--27 (1987; Zbl 0657.10043) OpenURL
Erdős, Paul Some problems on number theory. (English) Zbl 0615.10001 Combinatorics, graph theory, and computing, Proc. 17th Southeast. Conf., Boca Raton/Fl. 1986, Congr. Numerantium 54, 225-244 (1986). Reviewer: A.Ivić MSC: 11-02 11A41 11N05 11N37 00A07 PDF BibTeX XML OpenURL
Ivić, Aleksandar On squarefree numbers with restricted prime factors. (English) Zbl 0544.10043 Stud. Sci. Math. Hung. 20, 189-192 (1985). MSC: 11N05 PDF BibTeX XML Cite \textit{A. Ivić}, Stud. Sci. Math. Hung. 20, 189--192 (1985; Zbl 0544.10043) OpenURL
Hall, R. R. Squarefree numbers on short intervals. (English) Zbl 0502.10027 Mathematika 29, 7-17 (1982). MSC: 11N05 11N37 PDF BibTeX XML Cite \textit{R. R. Hall}, Mathematika 29, 7--17 (1982; Zbl 0502.10027) Full Text: DOI OpenURL
Montgomery, H. L.; Vaughan, R. C. The distribution of squarefree numbers. (English) Zbl 0462.10029 Recent progress in analytic number theory, Symp. Durham 1979, Vol. 1, 247-256 (1981). MSC: 11N05 11N37 PDF BibTeX XML OpenURL
Bellman, Richard Analytic number theory. An introduction. (English) Zbl 0448.10001 Mathematics Lecture Note Series, 57. Reading, Massachusetts, etc.: The Benjamin/Cummings Publishing Company, Inc., Advanced Book Program. 212 p. $ 19.50 (1980). MSC: 11-01 11-02 11A25 11N37 11M06 11N05 11N35 PDF BibTeX XML OpenURL
Kolesnik, G.; Straus, E. G. On the distribution of integers with a given number of prime factors. (English) Zbl 0446.10035 Acta Arith. 37, 181-199 (1980). MSC: 11N37 11N05 PDF BibTeX XML Cite \textit{G. Kolesnik} and \textit{E. G. Straus}, Acta Arith. 37, 181--199 (1980; Zbl 0446.10035) Full Text: DOI EuDML OpenURL
Warlimont, Richard Squarefree numbers in arithmetic progressions. (English) Zbl 0444.10036 J. Lond. Math. Soc., II. Ser. 22, 21-24 (1980). MSC: 11N13 11N05 PDF BibTeX XML Cite \textit{R. Warlimont}, J. Lond. Math. Soc., II. Ser. 22, 21--24 (1980; Zbl 0444.10036) Full Text: DOI OpenURL
Tanaka, Minoru Experiments concerning the distribution of squarefree numbers. (English) Zbl 0434.10029 Proc. Japan Acad., Ser. A 55, 101-105 (1979). Reviewer: William E. Briggs (Boulder) MSC: 11N25 11-04 PDF BibTeX XML Cite \textit{M. Tanaka}, Proc. Japan Acad., Ser. A 55, 101--105 (1979; Zbl 0434.10029) Full Text: DOI OpenURL
Erdős, Paul Some unconventional problems in number theory. (English) Zbl 0407.10001 Math. Mag. 52, 67-70 (1979). Reviewer: E.Härter MSC: 11-02 11A05 11A25 11N05 00A07 PDF BibTeX XML Cite \textit{P. Erdős}, Math. Mag. 52, 67--70 (1979; Zbl 0407.10001) Full Text: DOI Numdam OpenURL
Warlimont, Richard Eine Bemerkung über quadratfreie Zahlen \(\equiv 1\pmod k\). (German) Zbl 0404.10019 Monatsh. Math. 86, 333-336 (1979). Reviewer: Richard Warlimont (Regensburg) MSC: 11N25 PDF BibTeX XML Cite \textit{R. Warlimont}, Monatsh. Math. 86, 333--336 (1979; Zbl 0404.10019) Full Text: DOI EuDML OpenURL
Rieger, G. J. Remark on a paper of Stux concerning squarefree numbers in non-linear sequences. (English) Zbl 0395.10049 Pac. J. Math. 78, 241-242 (1978). MSC: 11N13 11N05 PDF BibTeX XML Cite \textit{G. J. Rieger}, Pac. J. Math. 78, 241--242 (1978; Zbl 0395.10049) Full Text: DOI OpenURL
Rieger, Georg Johann Number theory. (Zahlentheorie.) (German) Zbl 0328.10001 Studia Mathematica/Mathematische Lehrbücher. Band XXIX. Göttingen: Vandenhoeck & Ruprecht. 219 S. DM 39.00 (1976). Reviewer: Herbert Pieper (Berlin) MSC: 11-01 11Axx 11Mxx 11Jxx 11Pxx 11N05 11N13 11M06 11N35 11P05 PDF BibTeX XML OpenURL
Yüh, Ming-I On the differences between squarefree numbers. (English) Zbl 0083.04301 Science Record, n. Ser. 1, No. 3, 13-16 (1957). Reviewer: H.-E. Richert MSC: 11N25 PDF BibTeX XML Cite \textit{M.-I Yüh}, Science Record, n. Ser. 1, No. 3, 13--16 (1957; Zbl 0083.04301) OpenURL
Richert, Hans-Egon Über quadratfreie Zahlen mit genau \(r\) Primfaktoren in einer arithmetischen Progression. (German) Zbl 0052.04102 J. Reine Angew. Math. 192, 180-203 (1954). Reviewer: Sigmund Selberg MSC: 11N25 11N13 PDF BibTeX XML Cite \textit{H.-E. Richert}, J. Reine Angew. Math. 192, 180--203 (1954; Zbl 0052.04102) Full Text: Crelle EuDML OpenURL
Selberg, Sigmund Über die Verteilung einiger Klassen quadratfreier Zahlen, die aus einer gegebenen Anzahl von Primfaktoren zusammengesetzt sind. (German) Zbl 0028.01101 Skr. Norske Vid. Akad., Oslo. I. Mat.-Naturvid. Kl. No.5. Oslo: Jacob Dybwad. 49 S. (1942). MSC: 11N25 PDF BibTeX XML OpenURL
Landau, E. On some inequalities in the theory of Riemann zeta function. (Sur quelques inégalités dans la théorie de la fonction \(\zeta (s)\) de Riemann.) (French) JFM 36.0263.03 S. M. F. Bull. 33, 229-241 (1905). Reviewer: Fueter, Prof. (Basel) MSC: 11M06 11N25 PDF BibTeX XML Cite \textit{E. Landau}, Bull. Soc. Math. Fr. 33, 229--241 (1905; JFM 36.0263.03) Full Text: DOI Numdam EuDML OpenURL