A332626 Sum of least integers of prime signatures over all partitions of n into distinct parts.

1, 2, 4, 20, 40, 152, 664, 1760, 5680, 24752, 138064, 356480, 1568320, 5886752, 32781664, 266420000, 726928960, 3135277952, 16299729664, 81402739520, 640678081600, 7084434124352, 18897678264064, 92846198695040, 464088929482240, 3347512310365952

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..712

Eric Weisstein's World of Mathematics, Prime Signature

Wikipedia, Partition (number theory)

Wikipedia, Prime signature

Index entries for sequences related to prime signature

Formula

a(n) = Sum_{k=1..A000009(n)} A328524(n,k).

Example

a(5) = 2^5 + 2^4*3^1 + 2^3*3^2 = 32 + 48 + 72 = 152.

Maple

b:= proc(n, i, j) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
      1, b(n, i-1, j)+ithprime(j)^i*b(n-i, min(n-i, i-1), j+1)))
    end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..30);

Mathematica

b[n_, i_, j_] := b[n, i, j] = If[i(i+1)/2 < n, 0, If[n == 0, 1, b[n, i - 1, j] + Prime[j]^i b[n - i, Min[n - i, i - 1], j + 1]]];
a[n_] := b[n, n, 1];
a /@ Range[0, 30] (* Jean-François Alcover, May 04 2020, after Maple *)

Crossrefs

Row sums of A328524.

Cf. A000009, A025487, A074140.

Sequence in context: A259122 A059206 A294230 * A052004 A353342 A027741

Adjacent sequences: A332623 A332624 A332625 * A332627 A332628 A332629

Keyword

nonn

Author

Alois P. Heinz, Feb 17 2020

Status

approved