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Proceedings of the American Mathematical Society

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A prime-divisor function

Author: J. Knopfmacher
Journal: Proc. Amer. Math. Soc. 40 (1973), 373-377
MSC: Primary 10H25
MathSciNet review: 0327694
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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 [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 3rd ed., Clarendon Press, Oxford, 1954. MR 16, 673. MR 0067125 (16:673c)
  • [2] 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 9, 226. MR 0022569 (9:226c)
  • [3] J. Knopfmacher, Arithmetical properties of finite rings and algebras, and analytic number theory. II, J. Reine Angew. Math. 254 (1972), 74-99. MR 0364132 (51:387)
  • [4] J. Knopfmacher and J. Ridley, Prime-independent arithmetical functions, Ann. Mat. Pura Appl. (to appear). MR 0392872 (52:13685)
  • [5] P. G. Schmidt, Zur Anzahl Abelscher Gruppen gegebener Ordnung. II, Acta Arith. 13 (1967/68), 405-417. MR 37 #190. MR 0224591 (37:190)
  • [6] I. J. Schoenberg, On asymptotic distributions of arithmetical functions, Trans. Amer. Math. Soc. 39 (1936), 315-330. MR 1501849
  • [7] H. E. Richert, Über die Anzahl Abelscher Gruppen gegebener Ordnung. II, Math. Z. 58 (1953), 71-84. MR 14, 945. MR 0054594 (14:945d)

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Keywords: Asymptotic mean value, arithmetical progression, asymptotic distribution function, frequency, maximum order of magnitude
Article copyright: © Copyright 1973 American Mathematical Society

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