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A088881 If A056239(m) = n, then a(n) is the maximum value of A000005(m).

%I A088881 #18 Jul 23 2019 04:24:52
%S A088881 1,2,3,4,6,8,10,12,16,20,24,30,36,42,48,60,72,84,96,112,128,144,168,
%T A088881 192,224,256,288,336,384,432,480,540,600,672,768,864,960,1080,1200,
%U A088881 1320,1440,1620,1800,1980,2160,2400,2640,2880,3240,3600,3960,4320,4800,5280
%N A088881 If A056239(m) = n, then a(n) is the maximum value of A000005(m).
%C A088881 Maximum number of submultisets among all integer partitions of n. - _Gus Wiseman_, Jun 30 2019
%H A088881 Alois P. Heinz, <a href="/A088881/b088881.txt">Table of n, a(n) for n = 0..1000</a>
%e A088881 The partition (3,2,1,1,1) has 16 submultisets, which is more than for any other partition of 8, so a(8) = 16. - _Gus Wiseman_, Jun 30 2019
%p A088881 b:= proc(n, i) option remember; `if`(n=0 or i<2, n+1,
%p A088881        max(seq((j+1)*b(n-i*j, i-1), j=0..n/i)))
%p A088881     end:
%p A088881 a:= n-> b(n, n):
%p A088881 seq (a(n), n=0..100);  # _Alois P. Heinz_, Aug 09 2012
%t A088881 $RecursionLimit = 1000; b[n_, i_] :=  b[n, i] = If[n == 0 || i<2, n+1, Max[Table[ (j+1)*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table [a[n], {n, 0, 100}] (* _Jean-François Alcover_, Apr 15 2015, after _Alois P. Heinz_ *)
%t A088881 Table[Max@@(Times@@(1+Length/@Split[#])&)/@IntegerPartitions[n],{n,0,30}] (* _Gus Wiseman_, Jun 30 2019 *)
%Y A088881 Cf. A088880, A307699, A325694, A325798, A325828, A325830, A325831, A325832, A325833, A325834.
%K A088881 easy,nonn
%O A088881 0,2
%A A088881 _Naohiro Nomoto_, Nov 28 2003