A345283 a(n) = Sum_{p|n, p prime} p^nextprime(n/p), where nextprime(n) is the smallest prime > n.

0, 4, 9, 8, 25, 59, 49, 32, 243, 253, 121, 371, 169, 2391, 5312, 2048, 289, 4235, 361, 5173, 193954, 9523, 529, 185339, 78125, 133269, 177147, 147879, 841, 386344, 961, 131072, 1755374, 529201, 49651668, 2118611, 1369, 8395467, 129511456, 57216733, 1681, 138352314, 1849

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..43.

Example

a(12) = Sum_{p|12} p^nextprime(12/p) = 2^7 + 3^5 = 371.

Mathematica

Table[Sum[k^NextPrime[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]

Crossrefs

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

Sequence in context: A304203 A087687 A264090 * A369750 A365780 A297439

Adjacent sequences: A345280 A345281 A345282 * A345284 A345285 A345286

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved