A378548 Sum of divisors d of n such that n/d is odd with an even number of prime factors (counted with multiplicity).

1, 2, 3, 4, 5, 6, 7, 8, 10, 10, 11, 12, 13, 14, 16, 16, 17, 20, 19, 20, 22, 22, 23, 24, 26, 26, 30, 28, 29, 32, 31, 32, 34, 34, 36, 40, 37, 38, 40, 40, 41, 44, 43, 44, 53, 46, 47, 48, 50, 52, 52, 52, 53, 60, 56, 56, 58, 58, 59, 64, 61, 62, 73, 64, 66, 68, 67, 68, 70, 72, 71, 80, 73, 74, 83, 76, 78, 80, 79, 80, 91, 82

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Agrees with A378542 on odd n.

Dirichlet convolution of A000027 with A353557.

Dirichlet convolution of A000010 (Euler phi) with A369257.

Links

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

Crossrefs

Cf. A000010, A000203, A353557, A369257, A378526 (Dirichlet inverse), A378549.

Cf. also A002131, A378542, A378546.

Programs

PARI

A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A378548(n) = sumdiv(n,d,d*A353557(n/d));

Formula

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

a(n) = Sum_{d|n} A000010(n/d)*A369257(d).

a(n) = A000203(n) - A378549(n).