A351369 a(n) = Sum_{p|n, p prime} p * prime(p).

0, 6, 15, 6, 55, 21, 119, 6, 15, 61, 341, 21, 533, 125, 70, 6, 1003, 21, 1273, 61, 134, 347, 1909, 21, 55, 539, 15, 125, 3161, 76, 3937, 6, 356, 1009, 174, 21, 5809, 1279, 548, 61, 7339, 140, 8213, 347, 70, 1915, 9917, 21, 119, 61, 1018, 539, 12773, 21, 396, 125, 1288, 3167

Offset: 1

Author

Wesley Ivan Hurt, Feb 08 2022

Keywords

• nonn

Comments

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

Examples

			a(6) = 21; a(6) = Sum_{p|6} p * prime(p) = 2*3 + 3*5 = 21.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A010051, A033286, A061397, A351368.

Programs

Mathematica

Join[{0},Table[Total[# Prime[#]&/@FactorInteger[n][[;;,1]]],{n,2,80}]] (* Harvey P. Dale, Jan 28 2024 *)

Formula

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

a(p^k) = p * prime(p) for p prime and k>=1. - Wesley Ivan Hurt, Jul 16 2025