A378549 Sum of divisors d of n such that n/d is not an odd number with an even number of prime factors (counted with multiplicity).

0, 1, 1, 3, 1, 6, 1, 7, 3, 8, 1, 16, 1, 10, 8, 15, 1, 19, 1, 22, 10, 14, 1, 36, 5, 16, 10, 28, 1, 40, 1, 31, 14, 20, 12, 51, 1, 22, 16, 50, 1, 52, 1, 40, 25, 26, 1, 76, 7, 41, 20, 46, 1, 60, 16, 64, 22, 32, 1, 104, 1, 34, 31, 63, 18, 76, 1, 58, 26, 72, 1, 115, 1, 40, 41, 64, 18, 88, 1, 106, 30, 44, 1, 136, 22, 46, 32

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Agrees with A378543 on odd n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A000203, A353557, A378548.

Cf. also A378543, A378547.

Programs

PARI

A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A378549(n) = sumdiv(n,d,(1-A353557(d))*(n/d));

Formula

a(n) = Sum_{d|n} (1-A353557(d))*(n/d).

a(n) = A000203(n) - A378548(n).