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%I #9 Sep 22 2023 05:24:44
%S 0,1,0,1,3,4,6,10,13,20,27,36,52,71,94,126,170,216,286,367,473,603,
%T 771,963,1229,1529,1910,2371,2959,3623,4492,5487,6740,8200,10016,
%U 12099,14724,17722,21402,25687,30914,36892,44224,52630,62781,74497,88540,104646
%N a(n) = number of partitions p of n such that the least multiplicity of the parts of p is a part of p.
%F a(n) = A000041(n) - A365615(n).
%e 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 least multiplicities 1,1,1,1,1,1,5, respectively. The partitions that include least multiplicity as a part are [4,1], [3,1,1], [2,2,1], and [2,1,1,1], so that a(5) = 4.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n];
%t m[p_] := Min[Map[Length, Split[p]]]
%t Table[Count[f[n], p_ /; MemberQ[p, m[p]]], {n, 0, z}]
%Y Cf. A000041, A365613, A365615, A365616.
%K nonn
%O 0,5
%A _Clark Kimberling_, Sep 17 2023
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