A345282 a(n) = Sum_{p|n, p prime} p * nextprime(n/p).

0, 4, 6, 6, 10, 19, 14, 10, 15, 29, 22, 29, 26, 43, 46, 22, 34, 43, 38, 47, 68, 59, 46, 59, 35, 73, 33, 69, 58, 102, 62, 34, 94, 89, 104, 77, 74, 103, 116, 101, 82, 146, 86, 101, 106, 127, 94, 109, 77, 113, 142, 123, 106, 115, 142, 135, 164, 149, 118, 196, 122, 167, 146, 74, 176

Offset

1,2

Comments

If p is prime, a(p) = Sum_{p|p} p * nextprime(p/p) = 2*p.

Links

Table of n, a(n) for n=1..65.

Example

a(12) = Sum_{p|12} p * nextprime(12/p) = 2*7 + 3*5 = 14 + 15 = 29.

Mathematica

Table[Sum[k*NextPrime[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Cf. A151800 (nextprime v.2), A345280, A345281.

Sequence in context: A075653 A075656 A267573 * A369749 A193814 A304409

Adjacent sequences: A345279 A345280 A345281 * A345283 A345284 A345285

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved