A386594 a(n) = Sum_{d|n} d * c(n/d), where c = A351114.

1, 3, 4, 6, 5, 12, 7, 12, 12, 15, 11, 25, 13, 22, 21, 24, 17, 36, 19, 30, 28, 33, 23, 50, 25, 39, 36, 44, 29, 63, 31, 48, 44, 51, 36, 75, 37, 57, 52, 60, 41, 88, 43, 66, 63, 69, 47, 100, 49, 75, 68, 78, 53, 108, 55, 89, 76, 87, 59, 131, 61, 93, 84, 96, 65, 132, 67, 102, 92, 113, 71, 150, 73, 111, 105, 114, 77, 157, 79, 120, 108, 123, 83, 183, 85, 129, 116

Offset: 1

Author

Wesley Ivan Hurt, Jul 26 2025

Keywords

• nonn

Comments

Dirichlet convolution of n and c(n), where c = A351114.

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

Crossrefs

Cf. A020492 (balanced numbers), A351114.

Programs

Mathematica

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