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A341464 Number of partitions of n into 5 distinct nonprime parts.

%I A341464 #10 Jul 13 2021 16:59:48
%S A341464 1,1,1,1,2,2,4,4,5,7,7,9,12,14,15,19,21,27,29,35,38,47,49,59,65,77,82,
%T A341464 96,102,119,128,147,157,181,189,216,231,260,276,309,327,366,387,431,
%U A341464 454,505,529,584,617,678,713,780,818,892,938,1020,1071,1164,1213,1311,1378
%N A341464 Number of partitions of n into 5 distinct nonprime parts.
%p A341464 b:= proc(n, i, t) option remember; `if`(n=0,
%p A341464       `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p A341464       `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
%p A341464     end:
%p A341464 a:= n-> b(n$2, 5):
%p A341464 seq(a(n), n=28..88);  # _Alois P. Heinz_, Feb 12 2021
%t A341464 b[n_, i_, t_] := b[n, i, t] = If[n == 0,
%t A341464      If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
%t A341464      If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
%t A341464 a[n_] := b[n, n, 5];
%t A341464 Table[a[n], {n, 28, 88}] (* _Jean-François Alcover_, Jul 13 2021, after _Alois P. Heinz_ *)
%Y A341464 Cf. A005171, A018252, A096258, A219199, A302479, A341452, A341461, A341462, A341465, A341466, A341467.
%K A341464 nonn
%O A341464 28,5
%A A341464 _Ilya Gutkovskiy_, Feb 12 2021