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STRONG AND WEAK ATANASSOV PAIRS
P. SPIEGELHALTER,A. Zaharescu 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.3
We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = [수식],where [수식] is the prime factorization of n. We consider weighted combinations I(n)^aR(n)^b and characterize the pairs (a,b) 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)^aR(n)^b.