A378543 Sum of divisors d of n such that n/d has an odd number of prime factors (counted with multiplicity).

0, 1, 1, 2, 1, 5, 1, 5, 3, 7, 1, 11, 1, 9, 8, 10, 1, 16, 1, 15, 10, 13, 1, 25, 5, 15, 10, 19, 1, 32, 1, 21, 14, 19, 12, 35, 1, 21, 16, 35, 1, 42, 1, 27, 25, 25, 1, 51, 7, 36, 20, 31, 1, 50, 16, 45, 22, 31, 1, 72, 1, 33, 31, 42, 18, 62, 1, 39, 26, 60, 1, 80, 1, 39, 41, 43, 18, 72, 1, 71, 30, 43, 1, 94, 22, 45, 32, 65

Offset

1,4

Comments

Agrees with A378549 on odd n.

Dirichlet convolution of A000027 with A066829.

Dirichlet convolution of A000010 (Euler phi) with A056924.

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} A066829(n/d)*d.

a(n) = Sum_{d|n} A000010(n/d)*A056924(d).

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

Prog

(PARI) A378543(n) = sumdiv(n, d, d*!!(bigomega(n/d)%2));

Crossrefs

Cf. A000010, A000027, A000203, A056924, A066829, A378542.

Cf. also A378547, A378549.

Sequence in context: A390030 A379654 A060448 * A090080 A151737 A211361

Adjacent sequences: A378540 A378541 A378542 * A378544 A378545 A378546

Keyword

nonn

Author

Antti Karttunen, Dec 01 2024

Status

approved