A344459 a(n) = Sum_{d|n} d^Omega(d).

1, 3, 4, 19, 6, 42, 8, 531, 85, 108, 12, 1786, 14, 206, 234, 66067, 18, 5955, 20, 8124, 452, 498, 24, 334074, 631, 692, 19768, 22174, 30, 27372, 32, 33620499, 1104, 1176, 1238, 1687315, 38, 1466, 1538, 2568636, 42, 74774, 44, 85698, 91440, 2142, 48, 255203578, 2409

Offset: 1

Author

Wesley Ivan Hurt, May 19 2021

Keywords

• nonn

Comments

If p is prime, a(n) = Sum_{d|p} d^Omega(d) = 1^0 + p^1 = p + 1.

Inverse Möbius transform of n^Omega(n). - Wesley Ivan Hurt, Mar 31 2025

Examples

			a(8) = Sum_{d|8} d^Omega(d) = 1^0 + 2^1 + 4^2 + 8^3 = 531.
		

Crossrefs

Cf. A001222 (Omega).

Programs

Mathematica

Table[Sum[k^PrimeOmega[k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]