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Asymptotic behavior of the irrational factor

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Ledoan, A. H.
Zaharescu, Alexandru

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We study the irrational factor function I(n) introduced by Atanassov and defined by I(n) = Pi(k)(k=1)p(v)(1/alpha v), where n = Pi(k)(v=1) p(v)(alpha v) is the prime factorization of n. We show that the sequence {G(n)/n}(n >= 1), where G(n) = Pi(n)(v=1) I(v)(1/n), is covergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).

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Springer

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Mathematics

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Acta Mathematica Hungarica

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10.1007/s10474-008-7212-9

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