A351749 a(n) = Sum_{p|n, p prime} sigma_p(p).

0, 5, 28, 5, 3126, 33, 823544, 5, 28, 3131, 285311670612, 33, 302875106592254, 823549, 3154, 5, 827240261886336764178, 33, 1978419655660313589123980, 3131, 823572, 285311670617, 20880467999847912034355032910568, 33, 3126, 302875106592259

Offset: 1

Author

Wesley Ivan Hurt, Feb 17 2022

Keywords

• nonn

Comments

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

Examples

			a(6) = 33; a(6) = Sum_{p|6, p prime} sigma_p(p) = sigma_2(2) + sigma_3(3) = (1^2 + 2^2) + (1^3 + 3^3) = 33.
		

Crossrefs

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

Formula

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

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