A318674 Sum of squarefree divisors of n that have an even number of prime factors.

1, 1, 1, 1, 1, 7, 1, 1, 1, 11, 1, 7, 1, 15, 16, 1, 1, 7, 1, 11, 22, 23, 1, 7, 1, 27, 1, 15, 1, 32, 1, 1, 34, 35, 36, 7, 1, 39, 40, 11, 1, 42, 1, 23, 16, 47, 1, 7, 1, 11, 52, 27, 1, 7, 56, 15, 58, 59, 1, 32, 1, 63, 22, 1, 66, 62, 1, 35, 70, 60, 1, 7, 1, 75, 16, 39, 78, 72, 1, 11, 1, 83, 1, 42, 86, 87, 88, 23, 1, 32, 92, 47

Offset: 1

Author

Antti Karttunen, Sep 04 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A023900, A048250, A166142, A284118, A291784, A318675, A318676.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, MoebiusMu[#] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 06 2025 *)

PARI

A318674(n) = sumdiv(n,d,(1==moebius(d))*d);

Formula

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

a(n) = A048250(n) - A318675(n).

For all n >= 1, a(n) <= A318676(n).

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