A318676 Sum of divisors of n that have an even number of prime factors (counted with multiplicity).

1, 1, 1, 5, 1, 7, 1, 5, 10, 11, 1, 11, 1, 15, 16, 21, 1, 16, 1, 15, 22, 23, 1, 35, 26, 27, 10, 19, 1, 32, 1, 21, 34, 35, 36, 56, 1, 39, 40, 55, 1, 42, 1, 27, 25, 47, 1, 51, 50, 36, 52, 31, 1, 70, 56, 75, 58, 59, 1, 96, 1, 63, 31, 85, 66, 62, 1, 39, 70, 60, 1, 80, 1, 75, 41, 43, 78, 72, 1, 71, 91, 83, 1, 130, 86, 87, 88, 115, 1, 131, 92, 51

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

a(n) = Sum_{d|n} [A008836(d) > 0]*d.

a(n) = A000203(n) - A318677(n).

For all n >= 1, a(n) >= A318674(n).

a(n) = Sum_{d|n} d*A065043(d). - Antti Karttunen, Jan 24 2024

Mathematica

Array[DivisorSum[#, # &, EvenQ@ PrimeOmega@ # &] &, 92] (* Michael De Vlieger, Sep 04 2018 *)

Prog

(PARI) A318676(n) = sumdiv(n, d, (!(bigomega(d)%2))*d);

Crossrefs

Cf. A000203, A008836, A065043, A318674, A318677.

Cf. also A038548, A066839.

Sequence in context: A051712 A086892 A284150 * A346475 A346474 A353574

Adjacent sequences: A318673 A318674 A318675 * A318677 A318678 A318679

Keyword

nonn

Author

Antti Karttunen, Sep 04 2018

Status

approved