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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A161894 A062177 A129643 * A200337 A320931 A096421

Adjacent sequences:  A332641 A332642 A332643 * A332645 A332646 A332647

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 18 2020

STATUS

approved

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Last modified September 24 09:10 EDT 2021. Contains 347630 sequences. (Running on oeis4.)