A342996 The number of partitions of the n-th primorial.

1, 2, 11, 5604, 9275102575355, 21565010821742923705373368869534441911701199887419

Offset: 0

Author

Alois P. Heinz, Apr 01 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..7

Crossrefs

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

Programs

Maple

b:= proc(n) b(n):= `if`(n=0, 1, b(n-1)*ithprime(n)) end:
a:= n-> combinat[numbpart](b(n)):
seq(a(n), n=0..5);

Mathematica

b[n_] := b[n] = If[n == 0, 1, b[n - 1]*Prime[n]];
a[n_] := PartitionsP[b[n]];
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Jul 07 2021, from Maple *)

PARI

a(n) = numbpart(prod(k=1, n, prime(k))); \\ Michel Marcus, Jul 07 2021

Python

from sympy import primorial
from sympy.functions import partition
def A342996(n): return partition(primorial(n)) if n > 0 else 1 # Chai Wah Wu, Apr 03 2021

Formula

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