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A332644
Largest of the least integers of prime signatures over all partitions of n into distinct parts.
2
1, 2, 4, 12, 24, 72, 360, 720, 2160, 10800, 75600, 151200, 453600, 2268000, 15876000, 174636000, 349272000, 1047816000, 5239080000, 36673560000, 403409160000, 5244319080000, 10488638160000, 31465914480000, 157329572400000, 1101307006800000, 12114377074800000
OFFSET
0,2
FORMULA
a(n) = A328524(n,A000009(n)).
A001221(a(n)) = A003056(n).
A001222(a(n)) = n.
A046523(a(n)) = a(n).
a(n)/a(n-1) = A037126(n) = A000040(n-A000217(A003056(n))) for n > 0.
a(n) in { A025487 }.
a(n) in { A055932 }.
a(n) in { A087980 }.
A007814(a(n)) = A123578(n).
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 *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 18 2020
STATUS
approved