OFFSET
1,9
FORMULA
G.f.: x * (1 + Sum_{n>=1} a(n)*x^n/(1 + x^n)).
L.g.f.: log(Product_{n>=1} (1 + x^n)^(a(n)/n)) = Sum_{n>=1} a(n+1)*x^n/n.
MAPLE
with(numtheory): P:=proc(q) local a, d, n; a:=[1]:
for n from 1 to q do a:=[op(a), add((-1)^(n/d+1)*a[d], d=divisors(n))]:
od; op(a); end: P(74); # Paolo P. Lava, Apr 30 2019
MATHEMATICA
a[n_] := a[n] = Sum[(-1)^((n - 1)/d + 1) a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 75}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[a[k] x^k/(1 + x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 75}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 28 2019
STATUS
approved