A332684 a(n) = Sum_{k=1..n} mu(gcd(n, k)) * floor(n/k).

1, 1, 3, 3, 8, 2, 14, 7, 14, 5, 27, 6, 35, 7, 19, 18, 50, 5, 58, 16, 32, 14, 74, 14, 68, 15, 54, 29, 101, 3, 111, 39, 59, 21, 83, 26, 140, 24, 70, 39, 158, 6, 168, 51, 74, 32, 186, 29, 170, 20, 101, 66, 217, 17, 157, 64, 117, 39, 247, 28, 261, 39, 121, 92, 194

Offset: 1

Author

Ilya Gutkovskiy, Feb 19 2020

Keywords

• nonn

Comments

Moebius transform of A116477.

Moebius transform applied twice to A006218.

Crossrefs

Cf. A006218, A007427, A008683, A116477.

Programs

Mathematica

Table[Sum[MoebiusMu[GCD[n, k]] Floor[n/k], {k, 1, n}], {n, 1, 65}]
A007427[n_] := Sum[MoebiusMu[n/d] MoebiusMu[d], {d, Divisors[n]}]; A006218[n_] := Sum[DivisorSigma[0, k], {k, 1, n}]; Table[Sum[A007427[n/d] A006218[d], {d, Divisors[n]}], {n, 1, 65}]

PARI

a(n) = sum(k=1, n, moebius(gcd(n, k))*(n\k)); \\ Michel Marcus, Feb 21 2020

Formula

a(n) = Sum_{d|n} mu(n/d) * A116477(d).

a(n) = Sum_{d|n} A007427(n/d) * A006218(d).