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A300580
Number of partitions of n into prime power parts (not including 1) that do not divide n.
3
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
0,8
EXAMPLE
a(10) = 2 because we have [7, 3] and [4, 3, 3].
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 65}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 09 2018
STATUS
approved