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

24,5

Links

Table of n, a(n) for n=24..84.

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 *)

Crossrefs

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

Sequence in context: A156820 A104346 A318238 * A193450 A109906 A104856

Adjacent sequences: A341072 A341073 A341074 * A341076 A341077 A341078

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved