A351751 a(n) = Sum_{p|n, p prime} p^sigma_p(p).

0, 32, 22876792454961, 32

Offset: 1

Author

Wesley Ivan Hurt, Feb 17 2022

Keywords

• nonn

Comments

a(5) has 2185 digits.

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

Examples

			a(3) = 22876792454961; a(3) = Sum_{p|3, p prime} p^sigma_p(p) = 3^(1^3 + 3^3) = 3^28 = 22876792454961.
		

Crossrefs

Cf. A010051, A023887 (sigma_n(n)), A351749.

Formula

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