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A034893 Maximum of different products of partitions of n into distinct parts. 4
1, 1, 2, 3, 4, 6, 8, 12, 15, 24, 30, 40, 60, 72, 120, 144, 180, 240, 360, 420, 720, 840, 1008, 1260, 1680, 2520, 2880, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 22680, 40320, 45360, 51840, 60480, 72576, 90720, 120960, 181440, 201600, 362880, 403200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..1000 from T. D. Noe)

Tomislav Doslic, Maximum product over partitions into distinct parts, J. of Integer Sequences, Vol. 8 (2005), Article 05.5.8.

Andrew V. Sills, Robert Schneider, The product of parts or "norm" of a partition, arXiv:1904.08004 [math.NT], 2019. Also in Integers, (2020) Vol. 20A, Article #A13.

EXAMPLE

The partitions of n = 4 are (4), (1, 3), (2, 2), (1, 1, 2) and (1, 1, 1, 1) with the products of partitions being 4, 3, 4, 2 and 1 respectively. As these are 4 distinct numbers (being 1, 2, 3 and 4) we have a(4) = 4. - David A. Corneth, Apr 28 2020

MAPLE

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

     `if`(n=0, 1, max(b(n, i-1), i*b(n-i, min(n-i, i-1)))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 19 2019

MATHEMATICA

Table[Max[Times@@@Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]]<2&]], {n, 50}] (* Harvey P. Dale, May 28 2017 *)

b[n_, i_] := b[n, i] = If[i(i+1)/2<n, 0, If[n==0, 1, Max[b[n, i-1], i b[n-i, Min[n-i, i-1]]]]];

a[n_] := b[n, n];

Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Aug 21 2019, after Alois P. Heinz *)

CROSSREFS

Cf. A000792, A309859 (corresponding partitions).

Sequence in context: A081029 A300787 A171966 * A187448 A321266 A018662

Adjacent sequences:  A034890 A034891 A034892 * A034894 A034895 A034896

KEYWORD

nonn,nice

AUTHOR

Erich Friedman

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Apr 19 2019

STATUS

approved

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Last modified August 15 08:53 EDT 2020. Contains 336487 sequences. (Running on oeis4.)