A333051 a(1) = 1; a(n+1) = Sum_{d|n, gcd(d, n/d) = 1} a(n/d) * a(d).

1, 1, 2, 4, 8, 16, 36, 72, 144, 288, 592, 1184, 2384, 4768, 9608, 19248, 38496, 76992, 154272, 308544, 617152, 1234448, 2470080, 4940160, 9880608, 19761216, 39527200, 79054400, 158109088, 316218176, 632456976, 1264913952, 2529827904, 5059658176, 10119393344, 20238787264

Offset: 1

Author

Ilya Gutkovskiy, Mar 06 2020

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..3320

Crossrefs

Cf. A038044, A122698.

Programs

Maple

a[1]:= 1:
for n from 1 to 40 do
  P:= ifactors(n)[2];
  k:= nops(P);
  t:= 0;
  for S in combinat:-powerset(k) do
    d:= mul(P[i][1]^P[i][2],i=S);
    t:= t + a[d]*a[n/d]
  od;
  a[n+1]:= t
od:
seq(a[i],i=1..41); # Robert Israel, Mar 09 2020

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[If[GCD[(n - 1)/d, d] == 1, a[(n - 1)/d] a[d], 0], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 36}]