A369748 a(n) = Sum_{p|n, p prime} prime(n/p).

0, 2, 2, 3, 2, 8, 2, 7, 5, 14, 2, 20, 2, 20, 16, 19, 2, 36, 2, 36, 22, 34, 2, 56, 11, 44, 23, 50, 2, 89, 2, 53, 36, 62, 28, 98, 2, 70, 46, 90, 2, 129, 2, 86, 70, 86, 2, 142, 17, 126, 64, 108, 2, 164, 42, 126, 72, 112, 2, 221, 2, 130, 96, 131, 52, 229, 2, 146, 88, 221

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

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

Mathematica

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

Prog

(PARI) A369748(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, prime(n/f[i, 1]))); \\ Antti Karttunen, Jan 22 2025

Crossrefs

Cf. A000040, A010051, A351368.

Sequence in context: A225244 A345281 A338319 * A280583 A177047 A339665

Adjacent sequences: A369745 A369746 A369747 * A369749 A369750 A369751

Keyword

nonn,easy,changed

Author

Wesley Ivan Hurt, Jan 30 2024

Status

approved