A332644 Largest of the least integers of prime signatures over all partitions of n into distinct parts.

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

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) = 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 *)

Crossrefs

Subsequence of A025487, A055932, A087980.

Cf. A000009, A000040, A000217, A002110, A002260, A003056, A001221, A001222, A007814, A037126, A046523, A123578, A328524.

Sequence in context: A062177 A348642 A129643 * A200337 A367173 A367703

Adjacent sequences: A332641 A332642 A332643 * A332645 A332646 A332647

Keyword

nonn

Author

Alois P. Heinz, Feb 18 2020

Status

approved