A332626 - OEIS

%I #14 May 04 2020 07:04:51

%S 1,2,4,20,40,152,664,1760,5680,24752,138064,356480,1568320,5886752,

%T 32781664,266420000,726928960,3135277952,16299729664,81402739520,

%U 640678081600,7084434124352,18897678264064,92846198695040,464088929482240,3347512310365952

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

%H Alois P. Heinz, <a href="/A332626/b332626.txt">Table of n, a(n) for n = 0..712</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSignature.html">Prime Signature</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_signature">Prime signature</a>

%H <a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>

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

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

%p b:= proc(n, i, j) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,

%p       1, b(n, i-1, j)+ithprime(j)^i*b(n-i, min(n-i, i-1), j+1)))

%p     end:

%p a:= n-> b(n$2, 1):

%p seq(a(n), n=0..30);

%t 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]]];

%t a[n_] := b[n, n, 1];

%t a /@ Range[0, 30] (* _Jean-François Alcover_, May 04 2020, after Maple *)

%Y Row sums of A328524.

%Y Cf. A000009, A025487, A074140.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 17 2020