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

1,4

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.

Formula

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

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

Prog

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

Crossrefs

Cf. A000203, A353557, A378548.

Cf. also A378543, A378547.

Sequence in context: A111614 A193279 A378547 * A076889 A134689 A248029

Adjacent sequences: A378546 A378547 A378548 * A378550 A378551 A378552

Keyword

nonn,new

Author

Antti Karttunen, Dec 01 2024

Status

approved