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A369218
Number of partitions of n into prime power parts (including 1) not greater than sqrt(n).
1
1, 1, 1, 1, 3, 3, 4, 4, 5, 12, 14, 16, 19, 21, 24, 27, 64, 72, 84, 94, 108, 120, 136, 150, 169, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1342, 1469, 1602, 1747, 1898, 2062, 2233, 2418, 2611, 2818, 3034, 3266, 7529, 8185, 8884, 9632, 10427, 11276, 12177
OFFSET
0,5
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - Boole[k == 1 || PrimePowerQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 55}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 16 2024
STATUS
approved