A240176 Number of partitions of n such that (least part) > (multiplicity of least part).
1, 0, 1, 1, 1, 2, 3, 3, 5, 5, 8, 10, 13, 15, 21, 25, 31, 39, 50, 59, 75, 89, 111, 134, 164, 194, 240, 285, 344, 410, 493, 582, 699, 824, 981, 1157, 1369, 1606, 1901, 2223, 2613, 3054, 3579, 4166, 4871, 5658, 6590, 7645, 8877, 10264, 11900, 13733, 15868
Offset: 0
Examples
a(8) counts these 5 partitions: 8, 61, 53, 44, 332.
Programs
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Mathematica
z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Min[p] < Count[p, Min[p]]], {n, 0, z}] (* A240175 *) t2 = Table[Count[f[n], p_ /; Min[p] <= Count[p, Min[p]]], {n, 0, z}] (* A188216 *) t3 = Table[Count[f[n], p_ /; Min[p] == Count[p, Min[p]]], {n, 0, z}] (* A096403 *) t4 = Table[Count[f[n], p_ /; Min[p] > Count[p, Min[p]]], {n, 0, z}] (* A240176 *) t5 = Table[Count[f[n], p_ /; Min[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240177 *)