A286330 Number of partitions of n into a squarefree number of squarefree parts.
1, 1, 2, 3, 3, 5, 7, 10, 11, 15, 19, 26, 32, 42, 50, 66, 78, 101, 118, 150, 178, 224, 263, 327, 382, 471, 551, 670, 781, 944, 1098, 1317, 1526, 1821, 2105, 2498, 2879, 3399, 3908, 4592, 5266, 6164, 7056, 8220, 9388, 10897, 12424, 14368, 16342, 18843, 21394, 24585, 27858, 31932, 36119, 41277
Offset: 0
Keywords
Examples
a(8) = 11 because we have [7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [3, 3, 2], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1] and [2, 1, 1, 1, 1, 1, 1].
Programs
-
Mathematica
Join[{1}, Table[Length[Select[IntegerPartitions[n], SquareFreeQ[Length[#]] && AllTrue[#, SquareFreeQ] &]], {n, 55}]]