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

%I A266480 #27 May 28 2018 03:04:06
%S A266480 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,
%T A266480 108,120,135,150,165,180,200,220,240,264,288,312,336,364,405,450,495,
%U A266480 540,600,660,720,792,864,936,1008,1092,1176,1260,1365,1470,1575
%N A266480 Maximal product of multiplicities of parts of a partition of n.
%H A266480 Vaclav Kotesovec, <a href="/A266480/b266480.txt">Table of n, a(n) for n = 0..16000</a> (terms 0..5000 from Alois P. Heinz)
%e A266480 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.
%e A266480 a(21) = 7*4*2 = 56 for partition [1,1,1,1,1,1,1,2,2,2,2,3,3].
%p A266480 b:= proc(n, i) option remember; `if`(n=0 or i=1, max(1, n),
%p A266480       max(seq(b(n-i*j, i-1)*max(1, j), j=0..n/i)))
%p A266480     end:
%p A266480 a:= n-> b(n$2):
%p A266480 seq(a(n), n=0..100);
%t A266480 Table[Max@ Map[Times @@ Map[Last, Tally@ #] &, IntegerPartitions@ n], {n, 0, 56}] (* _Michael De Vlieger_, Dec 31 2015 *)
%t A266480 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_ *)
%Y A266480 Row lengths of A266477.
%Y A266480 Cf. A266871.
%K A266480 nonn
%O A266480 0,3
%A A266480 _Emeric Deutsch_ and _Alois P. Heinz_, Dec 29 2015