A369218 Number of partitions of n into prime power parts (including 1) not greater than sqrt(n).

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

Links

Table of n, a(n) for n=0..55.

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

Cf. A023893, A097356, A369219.

Sequence in context: A196179 A120188 A369217 * A097356 A083522 A355067

Adjacent sequences: A369215 A369216 A369217 * A369219 A369220 A369221

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 16 2024

Status

approved