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A327670 Sum of divisors of n that have an even number of distinct prime factors.

%I A327670 #8 Sep 27 2019 15:21:10
%S A327670 1,1,1,1,1,7,1,1,1,11,1,19,1,15,16,1,1,25,1,31,22,23,1,43,1,27,1,43,1,
%T A327670 32,1,1,34,35,36,73,1,39,40,71,1,42,1,67,61,47,1,91,1,61,52,79,1,79,
%U A327670 56,99,58,59,1,64,1,63,85,1,66,62,1,103,70,60,1,169,1,75,91
%N A327670 Sum of divisors of n that have an even number of distinct prime factors.
%H A327670 Alois P. Heinz, <a href="/A327670/b327670.txt">Table of n, a(n) for n = 1..20000</a>
%F A327670 G.f.: Sum_{k>=1} A030231(k) * x^A030231(k) / (1 - x^A030231(k)).
%F A327670 L.g.f.: log(B(x)) = Sum_{n>=1} a(n) * x^n / n, where B(x) = g.f. of A285798.
%F A327670 a(n) = A000203(n) - A327669(n).
%p A327670 with(numtheory):
%p A327670 a:= n-> add(`if`(nops(factorset(d))::even, d, 0), d=divisors(n)):
%p A327670 seq(a(n), n=1..80);  # _Alois P. Heinz_, Sep 21 2019
%t A327670 a[n_] := DivisorSum[n, # &, EvenQ[PrimeNu[#]] &]; Table[a[n], {n, 1, 75}]
%Y A327670 Cf. A000961 (positions of 1's), A000203, A030231, A049060, A285798, A318676, A327669.
%K A327670 nonn
%O A327670 1,6
%A A327670 _Ilya Gutkovskiy_, Sep 21 2019