A318675 Sum of squarefree divisors of n that have an odd number of prime factors.

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 5, 13, 9, 8, 2, 17, 5, 19, 7, 10, 13, 23, 5, 5, 15, 3, 9, 29, 40, 31, 2, 14, 19, 12, 5, 37, 21, 16, 7, 41, 54, 43, 13, 8, 25, 47, 5, 7, 7, 20, 15, 53, 5, 16, 9, 22, 31, 59, 40, 61, 33, 10, 2, 18, 82, 67, 19, 26, 84, 71, 5, 73, 39, 8, 21, 18, 96, 79, 7, 3, 43, 83, 54, 22, 45, 32, 13, 89, 40, 20, 25, 34, 49, 24, 5

Offset: 1

Author

Antti Karttunen, Sep 04 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A008472, A023900, A048250, A318320, A318674, A318677.

Programs

Mathematica

Array[DivisorSum[#, # &, MoebiusMu@ # == -1 &] &, 96] (* Michael De Vlieger, Sep 04 2018 *)

PARI

A318675(n) = sumdiv(n,d,(-1==moebius(d))*d);

Formula

For all n >= 1, a(n) <= A318677(n).

a(n) = Sum_{d|n} [A008683(d) < 0]*d.

a(n) = A048250(n) - A318674(n).

a(n) = (A048250(n) - A023900(n))/2. - Amiram Eldar, Jun 06 2025