A330106 Number of integer partitions of n whose product is a powerful number.
0, 0, 0, 0, 2, 2, 5, 5, 9, 11, 18, 19, 30, 36, 51, 62, 87, 104, 141, 171, 225, 271, 349, 419, 534, 643, 804, 965, 1197, 1431, 1766, 2106, 2571, 3063, 3719, 4410, 5325, 6305, 7567, 8939, 10678, 12572, 14961, 17567, 20804, 24389, 28775, 33626, 39551, 46106
Offset: 0
Keywords
Examples
The a(4) = 2 through a(10) = 18 partitions:
(4) (41) (33) (331) (8) (9) (55)
(22) (221) (42) (421) (44) (81) (82)
(222) (2221) (422) (333) (91)
(411) (4111) (2222) (441) (433)
(2211) (22111) (3311) (4221) (442)
(4211) (22221) (811)
(22211) (33111) (3322)
(41111) (42111) (3331)
(221111) (222111) (4222)
(411111) (4411)
(2211111) (22222)
(42211)
(222211)
(331111)
(421111)
(2221111)
(4111111)
(22111111)
Crossrefs
Programs
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Mathematica
powQ[n_]:=Min@@Last/@FactorInteger[n]>1; Table[Length[Select[IntegerPartitions[n],powQ[Times@@#]&]],{n,0,30}]