A327669 - OEIS

%I #8 Sep 27 2019 15:19:44

%S 0,2,3,6,5,5,7,14,12,7,11,9,13,9,8,30,17,14,19,11,10,13,23,17,30,15,

%T 39,13,29,40,31,62,14,19,12,18,37,21,16,19,41,54,43,17,17,25,47,33,56,

%U 32,20,19,53,41,16,21,22,31,59,104,61,33,19,126,18,82,67,23,26,84

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

%H Alois P. Heinz, <a href="/A327669/b327669.txt">Table of n, a(n) for n = 1..20000</a>

%F G.f.: Sum_{k>=1} A030230(k) * x^A030230(k) / (1 - x^A030230(k)).

%F L.g.f.: log(B(x)) = Sum_{n>=1} a(n) * x^n / n, where B(x) = g.f. of A285799.

%F a(n) = Sum_{d|n} d * A092248(d).

%F a(n) = A000203(n) - A327670(n).

%F a(p) = p, where p is prime.

%p with(numtheory):

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

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

%t a[n_] := DivisorSum[n, # &, OddQ[PrimeNu[#]] &]; Table[a[n], {n, 1, 70}]

%Y Cf. A000203, A030230, A049060, A092248, A285799, A318677, A327670.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Sep 21 2019