A318675 -id:A318675 - cp's OEIS frontend

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

Antti Karttunen, Sep 04 2018

nonn

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

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

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

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

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

A318677 Sum of divisors of n that have an odd number of prime factors (counted with multiplicity).

Original entry on oeis.org

0, 2, 3, 2, 5, 5, 7, 10, 3, 7, 11, 17, 13, 9, 8, 10, 17, 23, 19, 27, 10, 13, 23, 25, 5, 15, 30, 37, 29, 40, 31, 42, 14, 19, 12, 35, 37, 21, 16, 35, 41, 54, 43, 57, 53, 25, 47, 73, 7, 57, 20, 67, 53, 50, 16, 45, 22, 31, 59, 72, 61, 33, 73, 42, 18, 82, 67, 87, 26, 84, 71, 115, 73, 39, 83, 97, 18, 96, 79, 115, 30, 43, 83, 94, 22, 45, 32

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A008836, A318675, A318676.

Array[DivisorSum[#, # &, OddQ@ PrimeOmega@ # &] &, 87] (* Michael De Vlieger, Sep 04 2018 *)

A318677(n) = sumdiv(n,d,(bigomega(d)%2)*d);

a(n) = Sum_{d|n} [A008836(d) < 0]*d.
a(n) = A000203(n) - A318677(n).
For all n >= 1, a(n) >= A318675(n).

cp's OEIS Frontend

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

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