cp's OEIS Frontend

A067629 The average of the prime factors of n, rounded off to the nearest integer (rounding up if there's a choice), with each factor weighted according to its frequency of occurrence in the prime factorization.

%I A067629 #12 Jul 02 2025 16:02:01
%S A067629 2,3,2,5,3,7,2,3,4,11,2,13,5,4,2,17,3,19,3,5,7,23,2,5,8,3,4,29,3,31,2,
%T A067629 7,10,6,3,37,11,8,3,41,4,43,5,4,13,47,2,7,4,10,6,53,3,8,3,11,16,59,3,
%U A067629 61,17,4,2,9,5,67,7,13,5,71,2,73,20,4,8,9,6,79,3,3,22,83,4,11,23,16,4
%N A067629 The average of the prime factors of n, rounded off to the nearest integer (rounding up if there's a choice), with each factor weighted according to its frequency of occurrence in the prime factorization.
%H A067629 Hugo Pfoertner, <a href="/A067629/b067629.txt">Table of n, a(n) for n = 2..10000</a>
%e A067629 24 = 2^3 * 3^1, so the average of the prime factors = (2 + 2 + 2 + 3)/4, which rounded = 2. So a(24) = 2.
%p A067629 with(numtheory): for n from 2 to 150 do printf(`%d,`,round(sum(ifactors(n)[2][i][1]*ifactors(n)[2][i][2], i=1..nops(ifactors(n)[2]))/sum(ifactors(n)[2][i][2], i=1..nops(ifactors(n)[2]) ) )) od:
%t A067629 a[n_] := Floor[1/2+(Plus@@(Times@@#&/@(fn=FactorInteger[n])))/(Plus@@Last/@fn)]
%Y A067629 Cf. A078175, A126594.
%K A067629 easy,nonn
%O A067629 2,1
%A A067629 _Joseph L. Pe_, Feb 02 2002
%E A067629 Edited by _Dean Hickerson_ and _James Sellers_, Feb 12 2002