The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343119

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A343119

Number of compositions (ordered partitions) of the n-th primorial into distinct parts.
(history; published version)

#23 by Alois P. Heinz at Thu Apr 14 06:31:41 EDT 2022

STATUS

reviewed

approved

#22 by Michel Marcus at Thu Apr 14 02:11:29 EDT 2022

STATUS

proposed

reviewed

#21 by Jean-François Alcover at Thu Apr 14 02:08:08 EDT 2022

STATUS

editing

proposed

#20 by Jean-François Alcover at Thu Apr 14 02:07:53 EDT 2022

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 *)

STATUS

approved

editing

#19 by Alois P. Heinz at Fri Apr 09 15:33:17 EDT 2021

STATUS

editing

approved

#18 by Alois P. Heinz at Fri Apr 09 15:32:42 EDT 2021

COMMENTS

All terms are odd.

#17 by Alois P. Heinz at Fri Apr 09 15:26:37 EDT 2021

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);

#16 by Alois P. Heinz at Fri Apr 09 15:22:51 EDT 2021

LINKS

Alois P. Heinz, <a href="/A343119/b343119.txt">Table of n, a(n) for n = 0..6</a>

#15 by Alois P. Heinz at Fri Apr 09 15:20:20 EDT 2021

CROSSREFS

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

#14 by Alois P. Heinz at Fri Apr 09 15:19:35 EDT 2021

CROSSREFS

Cf. A002110, A032020, A342996, A343147.