A386574 Number of squarefree balanced divisors of n.

1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 3, 3, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 6, 1, 2, 2, 2, 2, 4, 1, 2, 2, 2, 1, 6, 1, 2, 3, 2, 1, 4, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 1, 6, 1, 2, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 2, 3, 2, 1, 5, 1, 2, 2, 2, 1, 6, 1, 2, 2, 2, 1, 6, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2

Offset: 1

Author

Wesley Ivan Hurt, Jul 26 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A005117 (squarefree numbers), A020492 (balanced numbers), A351114, A386573.

Programs

Mathematica

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

Formula

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