Department of Mathematics2024-11-1020080236-529410.1007/s10474-008-7212-92-s2.0-55049129774http://dx.doi.org/10.1007/s10474-008-7212-9https://hdl.handle.net/20.500.14288/17578We 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).MathematicsJournal Article1588-2632260468300006Q211020