A322527 Number of integer partitions of n whose product of parts is a power of a squarefree number (A072774).
1, 1, 2, 3, 5, 7, 11, 13, 18, 21, 31, 34, 45, 51, 63, 72, 88, 97, 120, 128, 158, 174, 201, 222, 264, 287, 333, 359, 416, 441, 518, 557, 631, 684, 770, 833, 954, 1017, 1141, 1222, 1378, 1475, 1643, 1755, 1939, 2097, 2327, 2471, 2758, 2928, 3233, 3470, 3813, 4085
Offset: 0
Keywords
Examples
The a(1) = 1 through a(8) = 18 integer partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (52) (44)
(111) (31) (41) (42) (61) (53)
(211) (221) (51) (331) (71)
(1111) (311) (222) (421) (422)
(2111) (321) (511) (521)
(11111) (411) (2221) (611)
(2211) (3211) (2222)
(3111) (4111) (3311)
(21111) (22111) (4211)
(111111) (31111) (5111)
(211111) (22211)
(1111111) (32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
Missing from the list for n = 7 through 9:
(43) (62) (54)
(322) (332) (63)
(431) (432)
(3221) (522)
(621)
(3222)
(3321)
(4311)
(32211)
Crossrefs
Programs
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Mathematica
Table[Length[Select[IntegerPartitions[n],SameQ@@Last/@FactorInteger[Times@@#]&]],{n,30}]