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%I #23 Nov 27 2023 18:23:59
%S 0,0,1,0,0,1,2,0,1,0,0,1,3,2,1,0,0,1,4,0,3,0,0,1,0,3,1,2,5,1,0,0,1,0,
%T 2,1,6,4,4,0,0,3,7,0,1,0,0,1,2,0,1,3,8,1,0,2,5,5,0,1,9,0,3,0,3,1,0,0,
%U 1,2,10,1,0,6,1,4,2,4,11,0,1,0,0,3,0,7,6,0,12,1,5,0,1,0,4,1,0,2,1
%N Sum of even indices of distinct prime factors of n divided by 2.
%F G.f.: Sum_{k>=1} k * x^prime(2*k) / (1 - x^prime(2*k)).
%e a(315) = 3 because 315 = 3^2 * 5 * 7 = prime(2)^2 * prime(3) * prime(4) and (2 + 4) / 2 = 3.
%t nmax = 100; CoefficientList[Series[Sum[k x^Prime[2 k]/(1 - x^Prime[2 k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y Cf. A066208 (positions of 0's), A066328, A324967, A332422, A344931, A366533, A366725.
%K nonn
%O 1,7
%A _Ilya Gutkovskiy_, Oct 24 2023