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

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

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.

Crossrefs

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

Cf. also A378547, A378549.

Programs

PARI

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

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).