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

%I A333051 #8 Mar 09 2020 11:32:39
%S A333051 1,1,2,4,8,16,36,72,144,288,592,1184,2384,4768,9608,19248,38496,76992,
%T A333051 154272,308544,617152,1234448,2470080,4940160,9880608,19761216,
%U A333051 39527200,79054400,158109088,316218176,632456976,1264913952,2529827904,5059658176,10119393344,20238787264
%N A333051 a(1) = 1; a(n+1) = Sum_{d|n, gcd(d, n/d) = 1} a(n/d) * a(d).
%H A333051 Robert Israel, <a href="/A333051/b333051.txt">Table of n, a(n) for n = 1..3320</a>
%p A333051 a[1]:= 1:
%p A333051 for n from 1 to 40 do
%p A333051   P:= ifactors(n)[2];
%p A333051   k:= nops(P);
%p A333051   t:= 0;
%p A333051   for S in combinat:-powerset(k) do
%p A333051     d:= mul(P[i][1]^P[i][2],i=S);
%p A333051     t:= t + a[d]*a[n/d]
%p A333051   od;
%p A333051   a[n+1]:= t
%p A333051 od:
%p A333051 seq(a[i],i=1..41); # _Robert Israel_, Mar 09 2020
%t A333051 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}]
%Y A333051 Cf. A038044, A122698.
%K A333051 nonn
%O A333051 1,3
%A A333051 _Ilya Gutkovskiy_, Mar 06 2020