A327670 - OEIS

%I #8 Sep 27 2019 15:21:10

%S 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 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 56,99,58,59,1,64,1,63,85,1,66,62,1,103,70,60,1,169,1,75,91

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

%H Alois P. Heinz, <a href="/A327670/b327670.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f.: Sum_{k>=1} A030231(k) * x^A030231(k) / (1 - x^A030231(k)).

%F L.g.f.: log(B(x)) = Sum_{n>=1} a(n) * x^n / n, where B(x) = g.f. of A285798.

%F a(n) = A000203(n) - A327669(n).

%p with(numtheory):

%p a:= n-> add(`if`(nops(factorset(d))::even, d, 0), d=divisors(n)):

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Sep 21 2019

%t a[n_] := DivisorSum[n, # &, EvenQ[PrimeNu[#]] &]; Table[a[n], {n, 1, 75}]

%Y Cf. A000961 (positions of 1's), A000203, A030231, A049060, A285798, A318676, A327669.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Sep 21 2019