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

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

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Formula

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

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

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

Maple

with(numtheory):
a:= n-> add(`if`(nops(factorset(d))::even, d, 0), d=divisors(n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Sep 21 2019

Mathematica

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

Crossrefs

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

Sequence in context: A284118 A165725 A214685 * A178637 A364092 A295294

Adjacent sequences: A327667 A327668 A327669 * A327671 A327672 A327673

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 21 2019

Status

approved