A369221 Number of compositions (ordered partitions) of n into prime power parts (not including 1) not greater than sqrt(n).

1, 0, 0, 0, 1, 0, 1, 0, 1, 5, 7, 9, 12, 16, 21, 28, 165, 241, 354, 518, 760, 1113, 1632, 2391, 3505, 14823, 22741, 34888, 53524, 82114, 125976, 193267, 296502, 454881, 697859, 1070626, 1642509, 2519868, 3865875, 5930862, 9098878, 13959114, 21415483, 32854729, 50404337, 77328204

Offset: 0

Author

Ilya Gutkovskiy, Jan 16 2024

Keywords

• nonn

Crossrefs

Cf. A280195, A364526.

Programs

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 45}]