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%I #14 Jul 08 2020 21:58:01
%S 2,1,3,2,3,4,3,4,3,5,4,5,4,5,6,5,6,5,6,5,7,6,7,6,7,6,7,8,7,8,7,8,7,8,
%T 7,9,8,9,8,9
%N Greatest number of distinct numbers in the intersection of p and its conjugate, as p ranges through the partitions of n.
%C Number of terms in row n of the array at A240181.
%C To match the definition, all terms need to be decreased by 1 (because the rows in A240181 start with k=0). So this appears to be an incorrect duplicate of A067731. - _Joerg Arndt_, Jul 30 2017
%t z = 30; conjugatePartition[part_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[part]; c = Map[BinCounts[#, {0, 1 + Max[#]}] &[Map[Length, Map[Intersection[#, conjugatePartition[#]] &, IntegerPartitions[#]]]] &, Range[z]]; Flatten[c] (* A240181 *)
%t Table[Length[c[[n]]], {n, 1, z}] (* A240450 *) (* _Peter J. C. Moses_, Apr 10 2014 *)
%Y Cf. A067731, A240181.
%K nonn,more
%O 1,1
%A _Clark Kimberling_, Apr 12 2014
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