A386573 Sum of the squarefree balanced divisors of n.

1, 3, 4, 3, 1, 12, 1, 3, 4, 3, 1, 12, 1, 17, 19, 3, 1, 12, 1, 3, 4, 3, 1, 12, 1, 3, 4, 17, 1, 57, 1, 3, 4, 3, 36, 12, 1, 3, 4, 3, 1, 68, 1, 3, 19, 3, 1, 12, 1, 3, 4, 3, 1, 12, 1, 17, 4, 3, 1, 57, 1, 3, 4, 3, 1, 12, 1, 3, 4, 122, 1, 12, 1, 3, 19, 3, 1, 90, 1, 3, 4, 3, 1, 68, 1, 3, 4, 3, 1, 57, 1, 3, 4, 3, 1, 12, 1, 17, 4, 3

Offset

1,2

Comments

Inverse Möbius transform of n * c(n) * mu(n)^2, where c = A351114.

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = Sum_{d|n} d * c(d) * mu(d)^2, where c = A351114.

Mathematica

Table[Sum[d (1 - Ceiling[DivisorSigma[1, d]/EulerPhi[d]] + Floor[DivisorSigma[1, d]/EulerPhi[d]]) MoebiusMu[d]^2, {d, Divisors[n]}], {n, 100}]

Crossrefs

Cf. A005117 (squarefree numbers), A020492 (balanced numbers), A078557, A351114, A386574.

Sequence in context: A279676 A279588 A279590 * A351113 A201935 A225445

Adjacent sequences: A386570 A386571 A386572 * A386574 A386575 A386576

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 26 2025

Status

approved