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
FORMULA
MAPLE
b:= proc(n, i, j) option remember;
`if`(i*(i+1)/2<n, 0, `if`(n=0, 1, max(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);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*
ithprime(n-(t-> t*(t+1)/2)(floor((sqrt(8*n-7)-1)/2))))
end:
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, Max[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 07 2020, after 1st Maple program *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 18 2020
STATUS
approved