A prime-divisor function
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- by J. Knopfmacher PDF
- Proc. Amer. Math. Soc. 40 (1973), 373-377 Request permission
Abstract:
This note studies the asymptotic mean values over arithmetical progressions, the general distribution of values, and the maximum order of magnitude, of a certain natural prime-divisor function of positive integers.References
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
- D. G. Kendall and R. A. Rankin, On the number of Abelian groups of a given order, Quart. J. Math. Oxford Ser. 18 (1947), 197–208. MR 22569, DOI 10.1093/qmath/os-18.1.197
- John Knopfmacher, Arithmetical properties of finite rings and algebras, and analytic number theory. II. Categories and analytic number theory, J. Reine Angew. Math. 254 (1972), 74–99. MR 364132, DOI 10.1515/crll.1972.254.74
- J. Knopfmacher and J. N. Ridley, Prime-independent arithmetical functions, Ann. Mat. Pura Appl. (4) 101 (1974), 153–169. MR 392872, DOI 10.1007/BF02417102
- Peter Georg Schmidt, Zur Anzahl Abelscher Gruppen gegebener Ordnung. II, Acta Arith 13 (1967/1968), 405–417 (German). MR 0224591, DOI 10.4064/aa-13-4-405-417
- I. J. Schoenberg, On asymptotic distributions of arithmetical functions, Trans. Amer. Math. Soc. 39 (1936), no. 2, 315–330. MR 1501849, DOI 10.1090/S0002-9947-1936-1501849-X
- Hans-Egon Richert, Über die Anzahl Abelscher Gruppen gegebener Ordnung. II, Math. Z. 58 (1953), 71–84 (German). MR 54594, DOI 10.1007/BF01174132
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 373-377
- MSC: Primary 10H25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0327694-7
- MathSciNet review: 0327694