A266480 - OEIS

%I #27 May 28 2018 03:04:06

%S 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 108,120,135,150,165,180,200,220,240,264,288,312,336,364,405,450,495,

%U 540,600,660,720,792,864,936,1008,1092,1176,1260,1365,1470,1575

%N Maximal product of multiplicities of parts of a partition of n.

%H 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 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 a(21) = 7*4*2 = 56 for partition [1,1,1,1,1,1,1,2,2,2,2,3,3].

%p b:= proc(n, i) option remember; `if`(n=0 or i=1, max(1, n),

%p       max(seq(b(n-i*j, i-1)*max(1, j), j=0..n/i)))

%p     end:

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

%p seq(a(n), n=0..100);

%t Table[Max@ Map[Times @@ Map[Last, Tally@ #] &, IntegerPartitions@ n], {n, 0, 56}] (* _Michael De Vlieger_, Dec 31 2015 *)

%t 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 Row lengths of A266477.

%Y Cf. A266871.

%K nonn

%O 0,3

%A _Emeric Deutsch_ and _Alois P. Heinz_, Dec 29 2015