A322526 Number of integer partitions of n whose product of parts is a squarefree number.

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

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: A218950 A193748 A364012 * A364232 A039852 A241068

Adjacent sequences: A322523 A322524 A322525 * A322527 A322528 A322529

Keyword

nonn

Author

Gus Wiseman, Dec 14 2018

Status

approved