A303365 Number of integer partitions of the n-th squarefree number using squarefree numbers.

1, 2, 3, 6, 9, 12, 28, 36, 60, 76, 96, 150, 228, 342, 416, 504, 877, 1484, 1759, 2079, 2885, 3387, 3968, 5413, 6304, 7328, 9852, 11395, 13159, 20082, 23056, 39532, 51385, 66488, 85660, 97078, 109907, 140465, 158573, 226918, 255268, 286920, 361606, 405470

Offset: 1

Author

Gus Wiseman, Apr 22 2018

Keywords

• nonn

Examples

			The a(5) = 9 partitions are (6), (51), (33), (321), (3111), (222), (2211), (21111), (111111).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000051, A005117, A072774, A073576, A078374, A302491, A302796, A303283, A303364.

Programs

Mathematica

nn=80;
sqf=Select[Range[nn],SquareFreeQ];
ser=Product[1/(1-x^sqf[[n]]),{n,Length[sqf]}];
Table[SeriesCoefficient[ser,{x,0,n}],{n,sqf}]

Formula

a(n) = A073576(A005117(n)).