A351368 a(n) = Sum_{p|n, p prime} prime(p).

0, 3, 5, 3, 11, 8, 17, 3, 5, 14, 31, 8, 41, 20, 16, 3, 59, 8, 67, 14, 22, 34, 83, 8, 11, 44, 5, 20, 109, 19, 127, 3, 36, 62, 28, 8, 157, 70, 46, 14, 179, 25, 191, 34, 16, 86, 211, 8, 17, 14, 64, 44, 241, 8, 42, 20, 72, 112, 277, 19, 283, 130, 22, 3, 52, 39, 331, 62, 88

Offset: 1

Author

Wesley Ivan Hurt, Feb 08 2022

Keywords

• nonn

Comments

Inverse Möbius transform of prime(n) * c(n), where c(n) is the characteristic function of primes (A010051). - Wesley Ivan Hurt, Jun 29 2024

Examples

			a(6) = 8; a(6) = Sum_{p|6, p prime} prime(p) = prime(2) + prime(3) = 3 + 5 = 8.
		

Crossrefs

Cf. A000040, A010051.

Programs

Mathematica

Table[DivisorSum[n, Prime[#] &, PrimeQ[#] &], {n, 100}] (* Wesley Ivan Hurt, Jun 29 2024 *)

Formula

From Wesley Ivan Hurt, Jun 29 2024: (Start)

a(n) = Sum_{d|n} prime(d) * c(d), where c = A010051.

a(p^k) = prime(p), for prime p and k >= 1. (End)