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%I #16 Nov 27 2023 18:23:38
%S 0,1,0,1,3,1,0,1,0,4,5,1,0,1,3,1,7,1,0,4,0,6,9,1,3,1,0,1,0,4,11,1,5,8,
%T 3,1,0,1,0,4,13,1,0,6,3,10,15,1,0,4,7,1,0,1,8,1,0,1,17,4,0,12,0,1,3,6,
%U 19,8,9,4,0,1,21,1,3,1,5,1,0,4,0,14,23,1,10,1,0,6,0,4,0,10,11,16,3,1,25,1,5,4
%N Sum of odd indices of distinct prime factors of n.
%F G.f.: Sum_{k>=1} (2*k-1) * x^prime(2*k-1) / (1 - x^prime(2*k-1)).
%e a(60) = 4 because 60 = 2^2 * 3 * 5 = prime(1)^2 * prime(2) * prime(3) and 1 + 3 = 4.
%t nmax = 100; CoefficientList[Series[Sum[(2 k - 1) x^Prime[2 k - 1]/(1 - x^Prime[2 k - 1]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A066207 (positions of 0's), A066328, A324966, A332422, A344908, A366528, A366784.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, Oct 24 2023
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