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

1,2

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.

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).

Prog

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

Crossrefs

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

Cf. also A378546, A378548.

Sequence in context: A048947 A342658 A222312 * A344404 A298676 A114519

Adjacent sequences: A378539 A378540 A378541 * A378543 A378544 A378545

Keyword

nonn,new

Author

Antti Karttunen, Dec 01 2024

Status

approved