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URL: https://oeis.org/A332626

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A332626
Sum of least integers of prime signatures over all partitions of n into distinct parts.
3
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
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.
Sequence in context: A383357 A059206 A294230 * A052004 A353342 A027741
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 17 2020
STATUS
approved