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%I #15 May 02 2022 03:32:45
%S 1,1,4,296,884987529,41144767887910339859917073881177514
%N The number of partitions of the n-th primorial into distinct parts.
%H Alois P. Heinz, <a href="/A343147/b343147.txt">Table of n, a(n) for n = 0..6</a>
%F a(n) = A000009(A002110(n)).
%p b:= proc(n) b(n):= `if`(n=0, 1, b(n-1)*ithprime(n)) end:
%p g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
%p `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
%p end:
%p a:= n-> g(b(n)):
%p seq(a(n), n=0..5);
%t $RecursionLimit = 2^13;
%t b[n_] := b[n] = If[n == 0, 1, b[n - 1]*Prime[n]];
%t g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j]*Sum[
%t If[OddQ[d], d, 0], {d, Divisors[j]}], {j, 1, n}]/n];
%t a[n_] := g[b[n]];
%t Table[a[n], {n, 0, 5}] (* _Jean-François Alcover_, May 02 2022, after _Alois P. Heinz_ *)
%Y Cf. A000009, A002110, A000849, A005867, A054640, A058254, A062447, A342996.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Apr 06 2021
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