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

%I #8 Jan 16 2022 15:34:08

%S 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,

%T 98,122,126,134,154,188,196,207,236,277,292,305,343,400,423,443,492,

%U 567,596,624,686,779,819,856,938,1052,1108,1149,1255,1394,1463,1515,1646,1818

%N Number of partitions of n into 6 distinct squarefree parts.

%p b:= proc(n, i, t) option remember; `if`(n=0,

%p `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+

%p `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))

%p end:

%p a:= n-> b(n$2, 6):

%p seq(a(n), n=24..84); # _Alois P. Heinz_, Feb 04 2021

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

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

%K nonn

%O 24,5

%A _Ilya Gutkovskiy_, Feb 04 2021