A369749 a(n) = Sum_{p|n, p prime} p * prime(n/p).

0, 4, 6, 6, 10, 19, 14, 14, 15, 37, 22, 47, 26, 55, 58, 38, 34, 85, 38, 93, 86, 95, 46, 131, 55, 121, 69, 135, 58, 246, 62, 106, 148, 169, 162, 233, 74, 191, 188, 237, 82, 366, 86, 235, 256, 235, 94, 337, 119, 339, 262, 293, 106, 389, 276, 347, 296, 305, 118, 624

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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

Mathematica

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

Crossrefs

Cf. A000040, A010051, A351368, A369748.

Sequence in context: A075656 A267573 A345282 * A193814 A304409 A081732

Adjacent sequences: A369746 A369747 A369748 * A369750 A369751 A369752

Keyword

nonn,easy,changed

Author

Wesley Ivan Hurt, Jan 30 2024

Status

approved