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A174524 The total number of factors in unordered factorizations of A025487(n).

%I A174524 #22 Jul 03 2025 09:28:52
%S A174524 0,1,3,3,6,8,12,17,10,20,22,34,27,35,46,61,60,54,94,75,107,37,101,123,
%T A174524 86,170,170,176,104,207,230,128,304,356,284,242,386,217,413,192,397,
%U A174524 506,303,434,680,442,512,698,502,703,275,847,832,151,725,818,1244,676,993,1190,1079,1162,399,1654,1311,446,1572,1501,1207,2158,1007,917,1840,1831,1980,2104,1785,1859,1579,556
%N A174524 The total number of factors in unordered factorizations of A025487(n).
%C A174524 A025487(n) has a certain number of unordered factorizations with between 1 and A001222(A025487(n)) factors.
%C A174524 a(n) counts these factors that are > 1. A025487(5) counts 8, 2*4, 2*2*2 with 1+2+3 = 6 = a(5) factors, for example.
%H A174524 Amiram Eldar, <a href="/A174524/b174524.txt">Table of n, a(n) for n = 1..10001</a>
%F A174524 a(n) = A066637(A025487(n)). - _R. J. Mathar_, Oct 03 2010
%e A174524 The table of factorizations in A162247 begins:
%e A174524   1
%e A174524   2
%e A174524   3
%e A174524   4 2 2
%e A174524   5
%e A174524   6 2 3
%e A174524   7
%e A174524   8 2 4 2 2 2
%e A174524   9 3 3
%e A174524   10 2 5
%e A174524   11
%e A174524   12 2 6 3 4 2 2 3
%e A174524 A025487(n) begins 1 2 4 6 8 12 ...
%e A174524 a(n) counts the elements larger than 1 in the A025487(n)-th row of A162247: 0 1 3 3 6 8 ...
%Y A174524 Cf. A001222, A025487, A066637, A162247.
%K A174524 nonn
%O A174524 1,3
%A A174524 _Alford Arnold_, Mar 21 2010
%E A174524 a(1) corrected and data extended by _R. J. Mathar_, Oct 03 2010