OFFSET
0,5
EXAMPLE
The partitions of 5 are [5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1], having greatest multiplicities 1,1,1,2,2,3,5, respectively. The partitions that include greatest multiplicity as a part are [4,1] and [2,2,1], so that a(5) = 2.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n];
m[p_] := Max[Map[Length, Split[p]]]
Table[Count[f[n], p_ /; MemberQ[p, m[p]]], {n, 0, z}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 17 2023
STATUS
approved