A343147 The number of partitions of the n-th primorial into distinct parts.

1, 1, 4, 296, 884987529, 41144767887910339859917073881177514

Offset: 0

Author

Alois P. Heinz, Apr 06 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..6

Crossrefs

Cf. A000009, A002110, A000849, A005867, A054640, A058254, A062447, A342996.

Programs

Maple

b:= proc(n) b(n):= `if`(n=0, 1, b(n-1)*ithprime(n)) end:
g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= n-> g(b(n)):
seq(a(n), n=0..5);

Mathematica

$RecursionLimit = 2^13;
b[n_] := b[n] = If[n == 0, 1, b[n - 1]*Prime[n]];
g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j]*Sum[
     If[OddQ[d], d, 0], {d, Divisors[j]}], {j, 1, n}]/n];
a[n_] := g[b[n]];
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, May 02 2022, after Alois P. Heinz *)

Formula

a(n) = A000009(A002110(n)).