A266480 Maximal product of multiplicities of parts of a partition of n.

1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 56, 64, 72, 84, 96, 108, 120, 135, 150, 165, 180, 200, 220, 240, 264, 288, 312, 336, 364, 405, 450, 495, 540, 600, 660, 720, 792, 864, 936, 1008, 1092, 1176, 1260, 1365, 1470, 1575

Offset: 0

Author

Emeric Deutsch and Alois P. Heinz, Dec 29 2015

Keywords

• nonn

Examples

			a(4) = 4 because the products of the multiplicities of the parts in the partitions [4], [1,3], [2,2], [1,1,2], [1,1,1,1] are 1, 1, 2, 2, 4, respectively.
a(21) = 7*4*2 = 56 for partition [1,1,1,1,1,1,1,2,2,2,2,3,3].
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..16000 (terms 0..5000 from Alois P. Heinz)

Crossrefs

Row lengths of A266477.

Cf. A266871.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, max(1, n),
      max(seq(b(n-i*j, i-1)*max(1, j), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..100);

Mathematica

Table[Max@ Map[Times @@ Map[Last, Tally@ #] &, IntegerPartitions@ n], {n, 0, 56}] (* Michael De Vlieger, Dec 31 2015 *)
b[n_, i_] := b[n, i] = If[n==0 || i==1, Max[1, n], Max[Table[b[n-i*j, i-1]*Max[1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 01 2016, after Alois P. Heinz *)