A346760 a(n) = Sum_{d|n} mu(n/d) * binomial(d,3).

0, 0, 1, 4, 10, 19, 35, 52, 83, 110, 165, 196, 286, 329, 444, 504, 680, 713, 969, 1016, 1294, 1375, 1771, 1752, 2290, 2314, 2841, 2908, 3654, 3476, 4495, 4400, 5290, 5304, 6500, 6124, 7770, 7467, 8852, 8688, 10660, 9802, 12341, 11700, 13652, 13409, 16215, 14768, 18389, 17190

Offset

1,4

Links

Table of n, a(n) for n=1..50.

Formula

G.f.: Sum_{k>=1} mu(k) * x^(3*k) / (1 - x^k)^4.

a(n) = (A059376(n) - 3 * A007434(n) + 2 * A000010(n)) / 6.

Mathematica

Table[Sum[MoebiusMu[n/d] Binomial[d, 3], {d, Divisors[n]}], {n, 1, 50}]
nmax = 50; CoefficientList[Series[Sum[MoebiusMu[k] x^(3 k)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(d, 3)); \\ Michel Marcus, Aug 03 2021

Crossrefs

3rd column of A020921.

Cf. A000010, A000292, A007434, A059376, A102309, A117108, A346761.

Sequence in context: A301215 A155389 A155316 * A038418 A301206 A057318

Adjacent sequences: A346757 A346758 A346759 * A346761 A346762 A346763

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved