A322530 Number of integer partitions of n with no 1's whose product of parts is a squarefree number.

1, 0, 1, 1, 0, 2, 1, 2, 1, 1, 3, 2, 2, 4, 3, 3, 3, 6, 5, 5, 5, 6, 8, 8, 9, 8, 11, 8, 12, 13, 16, 14, 13, 16, 21, 18, 21, 25, 22, 24, 27, 35, 33, 33, 32, 37, 42, 47, 48, 48, 52, 51, 59, 70, 68, 65, 69, 80, 87, 90, 103, 100, 96, 103, 123, 128, 135, 136, 132, 153

Offset

0,6

Comments

Such a partition must be strict and its parts must also be squarefree.

Links

Table of n, a(n) for n=0..69.

Example

The a(26) = 11 integer partitions:
  (26),
  (15,11), (19,7), (21,5), (23,3),
  (13,7,6), (13,10,3), (13,11,2), (17,7,2), (19,5,2),
  (11,7,5,3).

Mathematica

Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&SquareFreeQ[Times@@#]&]], {n, 30}]

Crossrefs

First differences of A322526.

Cf. A002865, A003963, A005117, A064573, A072774, A073576, A302505, A319005, A319057, A319169, A320322, A322527, A322528, A322529.

Sequence in context: A319814 A220272 A298917 * A303364 A131332 A059780

Adjacent sequences: A322527 A322528 A322529 * A322531 A322532 A322533

Keyword

nonn

Author

Gus Wiseman, Dec 14 2018

Status

approved