A327669 Sum of divisors of n that have an odd number of distinct prime factors.

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, 39, 13, 29, 40, 31, 62, 14, 19, 12, 18, 37, 21, 16, 19, 41, 54, 43, 17, 17, 25, 47, 33, 56, 32, 20, 19, 53, 41, 16, 21, 22, 31, 59, 104, 61, 33, 19, 126, 18, 82, 67, 23, 26, 84

Offset

1,2

Links

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

Formula

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

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

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

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

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

Maple

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

Mathematica

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

Crossrefs

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

Sequence in context: A100769 A353977 A023889 * A253413 A337355 A093783

Adjacent sequences: A327666 A327667 A327668 * A327670 A327671 A327672

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 21 2019

Status

approved