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

1,2

Links

Table of n, a(n) for n=1..44.

Formula

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

Example

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

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}]

Crossrefs

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

Sequence in context: A325552 A271882 A123316 * A096845 A285084 A248187

Adjacent sequences: A303362 A303363 A303364 * A303366 A303367 A303368

Keyword

nonn

Author

Gus Wiseman, Apr 22 2018

Status

approved