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

1,2

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.

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).

Prog

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

Crossrefs

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

Cf. also A002131, A378542, A378546.

Sequence in context: A073295 A191656 A266190 * A378546 A340625 A347644

Adjacent sequences: A378545 A378546 A378547 * A378549 A378550 A378551

Keyword

nonn

Author

Antti Karttunen, Dec 01 2024

Status

approved