A332685 a(n) = Sum_{k=1..n} mu(k/gcd(n, k)).

1, 2, 1, 2, 0, 2, 0, 0, -1, 0, 0, 0, -1, -2, -2, -3, 0, -4, -1, -5, -4, -2, 0, -8, -3, -4, -4, -7, 0, -8, -2, -10, -5, -4, -4, -13, 0, -5, -4, -13, 1, -15, -1, -9, -10, -5, -1, -22, -4, -12, -5, -11, -1, -19, -6, -17, -6, -4, 1, -28, 0, -8, -12, -18, -6, -19, 0, -12, -5, -17

Offset: 1

Author

Ilya Gutkovskiy, Feb 19 2020

Keywords

• sign

Comments

Inverse Moebius transform of A112399.

Links

• Ilya Gutkovskiy, Scatterplot of a(n) up to n=10000

Crossrefs

Cf. A002321, A007431, A007947, A008683, A063659, A112399, A276833, A304575.

Programs

Mathematica

Table[Sum[MoebiusMu[k/GCD[n, k]], {k, 1, n}], {n, 1, 70}]

PARI

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

Formula

a(n) = Sum_{k=1..n} mu(lcm(n, k)/n).

a(n) = Sum_{d|n} A112399(d).