A343119 Number of compositions (ordered partitions) of the n-th primorial into distinct parts.

1, 1, 11, 41867, 517934206090276988507, 42635439758725572299058305546953458030363703549127905691758491973278624456679699932948789006991639715987

Offset: 0

Author

Alois P. Heinz, Apr 09 2021

Keywords

• nonn

Comments

All terms are odd.

Links

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

Crossrefs

Cf. A002110, A032020, A000849, A005867, A054640, A058254, A062447, A342996, A343147.

Programs

Maple

b:= proc(n) b(n):= `if`(n=0, 1, b(n-1)*ithprime(n)) end:
g:= proc(n, k) option remember; `if`(k<0 or n<0, 0,
     `if`(k=0, `if`(n=0, 1, 0), g(n-k, k)+k*g(n-k, k-1)))
    end:
a:= n-> add(g(b(n), k), k=0..floor((sqrt(8*b(n)+1)-1)/2)):
seq(a(n), n=0..5);

Mathematica

$RecursionLimit = 5000;
b[n_] := If[n == 0, 1, b[n - 1]*Prime[n]];
g[n_, k_] := g[n, k] = If[k < 0 || n < 0, 0,
     If[k == 0, If[n == 0, 1, 0], g[n - k, k] + k*g[n - k, k - 1]]];
a[n_] := Sum[g[b[n], k], {k, 0, Floor[(Sqrt[8*b[n] + 1] - 1)/2]}];
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

Formula

a(n) = A032020(A002110(n)).