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A341073 Number of partitions of n into 4 distinct squarefree parts.

%I A341073 #12 Jul 14 2021 02:47:19
%S A341073 1,1,1,1,2,4,3,2,5,7,8,7,11,13,15,13,17,20,23,21,28,33,34,32,40,44,47,
%T A341073 44,55,63,66,62,75,84,87,81,98,110,115,109,127,144,148,140,159,180,
%U A341073 186,177,199,220,231,217,241,264,275,262,290,317,325,314,343,376,382,368,403
%N A341073 Number of partitions of n into 4 distinct squarefree parts.
%H A341073 Alois P. Heinz, <a href="/A341073/b341073.txt">Table of n, a(n) for n = 11..10000</a>
%p A341073 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341073       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341073       `if`(numtheory[issqrfree](i), b(n-i, min(n-i, i-1), t-1), 0)))
%p A341073     end:
%p A341073 a:= n-> b(n$2, 4):
%p A341073 seq(a(n), n=11..75);  # _Alois P. Heinz_, Feb 04 2021
%t A341073 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341073      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341073      If[SquareFreeQ[i], b[n - i, Min[n - i, i - 1], t - 1], 0]]];
%t A341073 a[n_] := b[n, n, 4];
%t A341073 Table[a[n], {n, 11, 75}] (* _Jean-François Alcover_, Jul 14 2021, after _Alois P. Heinz_ *)
%Y A341073 Cf. A005117, A008966, A098236, A307835, A308767, A341064, A341074, A341075, A341095, A341096, A341097, A341098.
%K A341073 nonn
%O A341073 11,5
%A A341073 _Ilya Gutkovskiy_, Feb 04 2021