A345280 a(n) = Sum_{p|n, p prime} nextprime(p), where nextprime(n) is the smallest prime > n.

0, 3, 5, 3, 7, 8, 11, 3, 5, 10, 13, 8, 17, 14, 12, 3, 19, 8, 23, 10, 16, 16, 29, 8, 7, 20, 5, 14, 31, 15, 37, 3, 18, 22, 18, 8, 41, 26, 22, 10, 43, 19, 47, 16, 12, 32, 53, 8, 11, 10, 24, 20, 59, 8, 20, 14, 28, 34, 61, 15, 67, 40, 16, 3, 24, 21, 71, 22, 34, 21, 73, 8, 79, 44

Offset

1,2

Comments

Inverse Möbius transform of nextprime(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Apr 01 2025

Links

Table of n, a(n) for n=1..74.

Formula

a(n) = Sum_{d|n} nextprime(d) * c(d), where c = A010051. - Wesley Ivan Hurt, Apr 01 2025

Example

a(15) = Sum_{p|15} nextprime(p) = nextprime(3) + nextprime(5) = 5 + 7 = 12.

Mathematica

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

Crossrefs

Cf. A010051, A151800 (nextprime v.2), A345281.

Sequence in context: A137769 A029602 A210041 * A240499 A248511 A210191

Adjacent sequences: A345277 A345278 A345279 * A345281 A345282 A345283

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved