A386622 a(n) = Sum_{d|n} n^c(d), where c = A351114.

1, 4, 6, 9, 6, 24, 8, 18, 19, 22, 12, 61, 14, 43, 46, 35, 18, 74, 20, 44, 44, 46, 24, 123, 27, 54, 56, 87, 30, 182, 32, 68, 68, 70, 72, 184, 38, 78, 80, 86, 42, 254, 44, 92, 138, 94, 48, 245, 51, 104, 104, 108, 54, 220, 58, 228, 116, 118, 60, 425, 62, 126, 130, 133, 68, 268, 68, 140, 140, 353, 72, 367, 74, 150, 228, 156, 80, 393, 80, 168, 165, 166, 84, 593

Offset: 1

Author

Wesley Ivan Hurt, Jul 27 2025

Keywords

• nonn

Crossrefs

Cf. A000005 (tau), A020492 (balanced numbers), A351112, A351114, A386591.

Programs

Mathematica

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

Formula

a(n) = tau(n) + (n - 1) * Sum_{d|n} c(d), where c = A351114.

a(n) = n*A351112(n) + A386591(n).