A300580 Number of partitions of n into prime power parts (not including 1) that do not divide n.

1, 0, 0, 0, 0, 1, 0, 3, 1, 3, 2, 11, 1, 18, 6, 9, 5, 43, 5, 65, 7, 31, 30, 137, 5, 115, 59, 84, 26, 379, 19, 519, 42, 213, 197, 323, 23, 1267, 340, 489, 50, 2213, 107, 2897, 221, 375, 938, 4871, 61, 3733, 662, 2193, 553, 10218, 409, 4241, 310, 4341, 3685, 20586, 154, 25792, 5635, 2862, 990, 12806

Offset: 0

Author

Ilya Gutkovskiy, Mar 09 2018

Keywords

• nonn

Examples

			a(10) = 2 because we have [7, 3] and [4, 3, 3].
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A023894, A098743, A128515, A246655, A284289, A300584.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 65}]