A345281 a(n) = Sum_{p|n} nextprime(n/p), where nextprime(m) is the smallest prime > m.

0, 2, 2, 3, 2, 8, 2, 5, 5, 10, 2, 12, 2, 14, 12, 11, 2, 18, 2, 16, 16, 16, 2, 24, 7, 20, 11, 22, 2, 35, 2, 17, 18, 22, 18, 32, 2, 26, 22, 34, 2, 47, 2, 28, 28, 32, 2, 46, 11, 40, 24, 34, 2, 48, 20, 40, 28, 34, 2, 67, 2, 40, 34, 37, 24, 67, 2, 42, 34, 65, 2, 66, 2, 44, 46, 46

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..76.

Example

a(20) = Sum_{p|20} nextprime(20/p) = nextprime(10) + nextprime(4) = 11 + 5 = 16.

Mathematica

Table[Sum[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.

Sequence in context: A248577 A015999 A225244 * A338319 A369748 A280583

Adjacent sequences: A345278 A345279 A345280 * A345282 A345283 A345284

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved