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This note studies the asymptotic mean values over arithmetical progressions, the general distribution of values, and the maximum order of magnitude, of a certain natural prime-divisor function of positive integers. Consider the multiplicative arithmetical function ß defined by /S(l) = l and ß(n) = axa2 ■ ■ ■ ocr if n=p\lp%% ■ ■ ■ plr (pt prime, oct>0). Kendall and Rankin [2, p. 199] pointed out that this function has the finite mean value y 1 V * * £(2)£(3) , 0", lim -> ß(n) =-= 1.943 • • •doi:10.2307/2039376 fatcat:joyinbbanjeilj6bztqbpk3kj4