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A338490 Sum of indices of distinct odd prime factors of n.

%I A338490 #24 Nov 10 2020 03:29:11
%S A338490 0,0,2,0,3,2,4,0,2,3,5,2,6,4,5,0,7,2,8,3,6,5,9,2,3,6,2,4,10,5,11,0,7,
%T A338490 7,7,2,12,8,8,3,13,6,14,5,5,9,15,2,4,3,9,6,16,2,8,4,10,10,17,5,18,11,
%U A338490 6,0,9,7,19,7,11,7,20,2,21,12,5,8,9,8,22,3,2,13,23,6,10,14,12,5,24,5
%N A338490 Sum of indices of distinct odd prime factors of n.
%H A338490 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A338490 G.f.: Sum_{k>=2} k * x^prime(k) / (1 - x^prime(k)).
%F A338490 a(n) = Sum_{p|n, p odd prime} A000720(p).
%F A338490 a(n) = A066328(A000265(n)).
%e A338490 a(60) = a(2^2 * 3 * 5) = a(prime(1)^2 * prime(2) * prime(3)) = 2 + 3 = 5.
%t A338490 nmax = 90; CoefficientList[Series[Sum[k x^Prime[k]/(1 - x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x] // Rest
%o A338490 (PARI) a(n) = vecsum(apply(primepi, (factor(n >> valuation(n, 2))[, 1]))); \\ _Michel Marcus_, Nov 10 2020
%Y A338490 Cf. A000265, A000720, A005069, A005087, A056239, A066328.
%K A338490 nonn
%O A338490 1,3
%A A338490 _Ilya Gutkovskiy_, Nov 09 2020