%I #22 Jul 07 2021 10:57:43

%S 1,2,11,5604,9275102575355,

%T 21565010821742923705373368869534441911701199887419

%N The number of partitions of the n-th primorial.

%H Alois P. Heinz, <a href="/A342996/b342996.txt">Table of n, a(n) for n = 0..7</a>

%F a(n) = A000041(A002110(n)).

%p b:= proc(n) b(n):= `if`(n=0, 1, b(n-1)*ithprime(n)) end:

%p a:= n-> combinat[numbpart](b(n)):

%p seq(a(n), n=0..5);

%t b[n_] := b[n] = If[n == 0, 1, b[n - 1]*Prime[n]];

%t a[n_] := PartitionsP[b[n]];

%t Table[a[n], {n, 0, 5}] (* _Jean-François Alcover_, Jul 07 2021, from Maple *)

%o (Python)

%o from sympy import primorial

%o from sympy.functions import partition

%o def A342996(n): return partition(primorial(n)) if n > 0 else 1 # _Chai Wah Wu_, Apr 03 2021

%o (PARI) a(n) = numbpart(prod(k=1, n, prime(k))); \\ _Michel Marcus_, Jul 07 2021

%Y Cf. A000041, A002110, A000849, A005867, A054640, A058254, A062447, A343147.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Apr 01 2021