Strong and weak Atanassov pairs

P. Spiegelhalter; Alexandru Zaharescu

Strong and weak Atanassov pairs

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = Π^k_v=1 p^1/ar_v' and R(n) = Π^k_v=1 P _v^αν-1 where n = Π^k_v=1 p_v^αv is the prime factorization of n. We consider weighted combinations 7(n)^o R(n)^β and characterize the pairs (α,β) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I (n)ⁿ R(n)^β.

Original language	English (US)
Pages (from-to)	355-361
Number of pages	7
Journal	Proceedings of the Jangjeon Mathematical Society
Volume	14
Issue number	3
State	Published - Jul 2011

Keywords

Arithmetic functions
Irrational factor
Restrictive factor
Riemann zeta-function

ASJC Scopus subject areas

Mathematics(all)

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AU - Zaharescu, Alexandru

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N2 - We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = Πkv=1 p1/arv' and R(n) = Πkv=1 P vαν-1 where n = Πkv=1 pvαv is the prime factorization of n. We consider weighted combinations 7(n)o R(n)β and characterize the pairs (α,β) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I (n)n R(n)β.

AB - We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = Πkv=1 p1/arv' and R(n) = Πkv=1 P vαν-1 where n = Πkv=1 pvαv is the prime factorization of n. We consider weighted combinations 7(n)o R(n)β and characterize the pairs (α,β) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I (n)n R(n)β.

KW - Arithmetic functions

KW - Irrational factor

KW - Restrictive factor

KW - Riemann zeta-function

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SN - 1598-7264

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JF - Proceedings of the Jangjeon Mathematical Society

IS - 3

ER -

Strong and weak Atanassov pairs

Abstract

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