A369743 a(n) = Sum_{p|n, p prime} p * Omega(n/p).

0, 0, 0, 2, 0, 5, 0, 4, 3, 7, 0, 10, 0, 9, 8, 6, 0, 10, 0, 14, 10, 13, 0, 15, 5, 15, 6, 18, 0, 20, 0, 8, 14, 19, 12, 15, 0, 21, 16, 21, 0, 24, 0, 26, 16, 25, 0, 20, 7, 14, 20, 30, 0, 15, 16, 27, 22, 31, 0, 30, 0, 33, 20, 10, 18, 32, 0, 38, 26, 28, 0, 20, 0, 39, 16

Offset

1,4

Comments

Dirichlet convolution of n*c(n) and Omega(n), where c = A010051. - Wesley Ivan Hurt, Jun 24 2026

Links

Table of n, a(n) for n=1..75.

Formula

a(p^k) = p*(k-1), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

a(n) = Sum_{d|n} d*c(d)*Omega(n/d), where c = A010051. - Wesley Ivan Hurt, Jun 24 2026

Mathematica

Table[DivisorSum[n, #*PrimeOmega[n/#] &, PrimeQ[#] &], {n, 100}]

Crossrefs

Cf. A001222 (Omega), A010051, A329347, A369741.

Sequence in context: A318889 A319853 A228620 * A374941 A369907 A257013

Adjacent sequences: A369740 A369741 A369742 * A369744 A369745 A369746

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 30 2024

Status

approved