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A341453 Number of partitions of n into 6 nonprime parts.

%I A341453 #13 Feb 21 2023 16:55:20
%S A341453 1,0,0,1,0,1,1,1,2,2,2,3,3,4,6,6,7,9,10,12,15,16,20,23,27,30,36,40,48,
%T A341453 53,62,68,81,87,105,112,130,141,166,176,208,219,256,271,314,331,385,
%U A341453 403,468,488,561,588,674,702,804,837,952,991,1126,1168,1321,1372
%N A341453 Number of partitions of n into 6 nonprime parts.
%p A341453 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341453       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341453       `if`(isprime(i), 0, b(n-i, min(n-i, i), t-1))))
%p A341453     end:
%p A341453 a:= n-> b(n$2, 6):
%p A341453 seq(a(n), n=6..67);  # _Alois P. Heinz_, Feb 12 2021
%t A341453 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341453      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341453      If[PrimeQ[i], 0, b[n - i, Min[n - i, i], t - 1], 0]]];
%t A341453 a[n_] := b[n, n, 6];
%t A341453 Table[a[n], {n, 6, 67}] (* _Jean-François Alcover_, Feb 23 2022, after _Alois P. Heinz_ *)
%t A341453 Table[Count[IntegerPartitions[n,{6}],_?(NoneTrue[#,PrimeQ]&)],{n,6,70}] (* _Harvey P. Dale_, Feb 21 2023 *)
%Y A341453 Cf. A002095, A005171, A018252, A062610, A259196, A341408, A341451, A341452, A341454, A341455, A341457.
%K A341453 nonn
%O A341453 6,9
%A A341453 _Ilya Gutkovskiy_, Feb 12 2021