A378542 Sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).

1, 2, 3, 5, 5, 7, 7, 10, 10, 11, 11, 17, 13, 15, 16, 21, 17, 23, 19, 27, 22, 23, 23, 35, 26, 27, 30, 37, 29, 40, 31, 42, 34, 35, 36, 56, 37, 39, 40, 55, 41, 54, 43, 57, 53, 47, 47, 73, 50, 57, 52, 67, 53, 70, 56, 75, 58, 59, 59, 96, 61, 63, 73, 85, 66, 82, 67, 87, 70, 84, 71, 115, 73, 75, 83, 97, 78, 96, 79, 115, 91

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Agrees with A378548 on odd n.

Dirichlet convolution of A000027 with A065043.

Dirichlet convolution of A000010 (Euler phi) with A038548.

Links

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

Crossrefs

Cf. A000010, A000027, A000203, A001222, A038548, A065043, A378525 (Dirichlet inverse), A378543.

Cf. also A378546, A378548.

Programs

PARI

A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));

Formula

a(n) = Sum_{d|n} A065043(n/d)*d.

a(n) = Sum_{d|n} A000010(n/d)*A038548(d).

a(n) = A000203(n) - A378543(n).