A prime-divisor function
نویسندگان
چکیده
منابع مشابه
On an Additive Prime Divisor Function of Alladi and Erdős
This paper discusses the additive prime divisor function A(n) := ∑ pα||n αp which was introduced by Alladi and Erdős in 1977. It is shown that A(n) is uniformly distributed (mod q) for any fixed integer q > 1.
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provided x is sufficiently large. An asymptotic formula of type (1) Df (x; q, a) = (1 +O((log x)))Df (x; q) , in which the error term is smaller than the main term by a suitable power of log x, is good enough for basic applications. More important than the size of the error term is the range where (1) holds uniformly with respect to the modulus q. In this paper we consider the problem for the d...
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Wemodify the recent method of J.-M. Deshouillers and H. Iwaniec in the theory of uniform distribution to show that the sequence with general term an = 1 n ∑ m≤n σ(m) is uniformly distributed modulo 1. We also study uniform distribution modulo 1 of some sequences related by the functions σ and φ. AMS subject classifications: 11K65, 11K31, 11J71, 11N36, 11N64
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0327694-7