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A327670
Sum of divisors of n that have an even number of distinct prime factors.
2
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 21 2019
STATUS
approved