A347655 Number of partitions of n into at most 4 squarefree parts.
1, 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 17, 19, 22, 24, 28, 31, 34, 37, 42, 44, 50, 53, 59, 61, 69, 71, 80, 82, 90, 93, 103, 106, 117, 121, 134, 137, 150, 154, 169, 173, 188, 194, 212, 216, 235, 240, 259, 264, 284, 288, 310, 314, 337, 342, 368, 370, 398, 403, 432
Offset: 0
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Mathematica
Table[Count[IntegerPartitions[n,4],?(AllTrue[#,SquareFreeQ]&)],{n,0,100}] (* _Harvey P. Dale, Sep 04 2023 *)