OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
Convolution inverse of A061256.
a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A001001(k)*a(n-k) for n > 0.
G.f.: exp(-Sum_{k>=1} sigma_2(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 29 2018
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
d*sigma(d), d=divisors(j))*b(n-j), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i)*a(i), i=0..n-1))
end:
seq(a(n), n=0..45); # Alois P. Heinz, Jun 08 2017
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*DivisorSigma[1, d], {d,
Divisors[j]}]*b[n - j], {j, 1, n}]/n];
a[n_] := a[n] = If[n == 0, 1, -Sum[b[n - i]*a[i], {i, 0, n - 1}]];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Mar 02 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 08 2017
STATUS
approved