A341075 Number of partitions of n into 6 distinct squarefree parts.

1, 0, 0, 1, 2, 2, 2, 3, 6, 5, 6, 7, 12, 12, 15, 18, 26, 26, 28, 34, 44, 46, 50, 60, 77, 79, 86, 98, 122, 126, 134, 154, 188, 196, 207, 236, 277, 292, 305, 343, 400, 423, 443, 492, 567, 596, 624, 686, 779, 819, 856, 938, 1052, 1108, 1149, 1255, 1394, 1463, 1515, 1646, 1818

Offset: 24

Author

Ilya Gutkovskiy, Feb 04 2021

Keywords

• nonn

Crossrefs

Cf. A005117, A008966, A098236, A307835, A308902, A341066, A341073, A341074, A341095, A341096, A341097, A341098.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
    end:
a:= n-> b(n$2, 6):
seq(a(n), n=24..84);  # Alois P. Heinz, Feb 04 2021

Mathematica

Table[Length[Select[IntegerPartitions[n,{6}],Length[Union[#]]==6&&AllTrue[ #,SquareFreeQ]&]],{n,24,90}] (* Harvey P. Dale, Jan 16 2022 *)