A369219 Number of partitions of n into prime power parts (not including 1) not greater than sqrt(n).
1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 2, 3, 2, 3, 3, 10, 8, 12, 10, 14, 12, 16, 14, 19, 44, 50, 53, 60, 63, 71, 74, 83, 87, 96, 101, 111, 116, 127, 133, 145, 151, 164, 171, 185, 193, 207, 216, 232, 612, 656, 699, 748, 795, 849, 901, 960, 1017, 1081, 1144, 1214, 1282, 1358, 1433, 3620, 3845
Offset: 0
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Programs
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Mathematica
Table[SeriesCoefficient[Product[1/(1 - Boole[PrimePowerQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 65}]