

A322526


Number of integer partitions of n whose product of parts is a squarefree number.


8



1, 1, 2, 3, 3, 5, 6, 8, 9, 10, 13, 15, 17, 21, 24, 27, 30, 36, 41, 46, 51, 57, 65, 73, 82, 90, 101, 109, 121, 134, 150, 164, 177, 193, 214, 232, 253, 278, 300, 324, 351, 386, 419, 452, 484, 521, 563, 610, 658, 706, 758, 809, 868, 938, 1006, 1071, 1140, 1220, 1307
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OFFSET

0,3


COMMENTS

The parts of such a partition must also be squarefree and distinct except for any number of 1's.


LINKS

Table of n, a(n) for n=0..58.


EXAMPLE

The a(8) = 9 partitions are (53), (71), (521), (611), (5111), (32111), (311111), (2111111), (11111111). Missing from this list are (8), (62), (44), (431), (422), (4211), (41111), (332), (3311), (3221), (2222), (22211), (221111).


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], SquareFreeQ[Times@@#]&]], {n, 30}]


CROSSREFS

Partial sums of A322530.
Cf. A001055, A003963, A005117, A064573 , A073576, A096276, A301987, A302505, A319005, A319916, A320322, A322527, A322529, A322531.
Sequence in context: A338886 A218950 A193748 * A039852 A241068 A035938
Adjacent sequences: A322523 A322524 A322525 * A322527 A322528 A322529


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 14 2018


STATUS

approved



