A386595 a(n) = Sum_{d|n} sigma(d)/phi(d) * c(d), where c = A351114.

1, 4, 3, 4, 1, 12, 1, 4, 3, 4, 1, 19, 1, 8, 6, 4, 1, 12, 1, 4, 3, 4, 1, 19, 1, 4, 3, 8, 1, 24, 1, 4, 3, 4, 3, 19, 1, 4, 3, 4, 1, 24, 1, 4, 6, 4, 1, 19, 1, 4, 3, 4, 1, 12, 1, 13, 3, 4, 1, 31, 1, 4, 3, 4, 1, 12, 1, 4, 3, 16, 1, 19, 1, 4, 6, 4, 1, 19, 1, 4, 3, 4, 1, 31, 1, 4, 3, 4, 1, 24, 1, 4, 3, 4, 1, 19, 1, 8, 3, 4

Offset: 1

Author

Wesley Ivan Hurt, Jul 26 2025

Keywords

• nonn

Comments

For each divisor d of n, add sigma(d)/phi(d) if phi(d) | sigma(d), else add 0.

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A351114.

Programs

Mathematica

Table[Sum[(DivisorSigma[1, d]/EulerPhi[d])*(1 - Ceiling[DivisorSigma[1, d]/EulerPhi[d]] + Floor[DivisorSigma[1, d]/EulerPhi[d]]), {d, Divisors[n]}], {n, 100}]