A332466 a(n) = n! * Sum_{d|n} mu(d) / d!.

1, 1, 5, 12, 119, 241, 5039, 20160, 302400, 1784161, 39916799, 160332480, 6227020799, 43571848321, 1078831353601, 10461394944000, 355687428095999, 2143016754278400, 121645100408831999, 1196177491129420800, 42565648051390464001, 562000335730215782401

Offset: 1

Author

Ilya Gutkovskiy, Feb 13 2020

Keywords

• nonn

Crossrefs

Cf. A008683, A057625, A068107, A099740, A132958, A332467.

Programs

Maple

with(numtheory):
a:= n-> n! * add(mobius(d)/d!, d=divisors(n)):
seq(a(n), n=1..23);  # Alois P. Heinz, Feb 13 2020

Mathematica

Table[n! DivisorSum[n, MoebiusMu[#]/#! &], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] x^k/(k! (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

PARI

a(n)={sumdiv(n, d, moebius(d)*n!/d!)} \\ Andrew Howroyd, Feb 13 2020

Formula

E.g.f.: Sum_{k>=1} Sum_{j>=1} mu(j) * x^(k*j) / j!.

E.g.f.: Sum_{k>=1} mu(k) * x^k / (k!*(1 - x^k)).