%I #10 Jul 13 2021 16:59:48

%S 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 96,102,119,128,147,157,181,189,216,231,260,276,309,327,366,387,431,

%U 454,505,529,584,617,678,713,780,818,892,938,1020,1071,1164,1213,1311,1378

%N Number of partitions of n into 5 distinct nonprime 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`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))

%p end:

%p a:= n-> b(n$2, 5):

%p seq(a(n), n=28..88); # _Alois P. Heinz_, Feb 12 2021

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0,

%t If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +

%t If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];

%t a[n_] := b[n, n, 5];

%t Table[a[n], {n, 28, 88}] (* _Jean-François Alcover_, Jul 13 2021, after _Alois P. Heinz_ *)

%Y Cf. A005171, A018252, A096258, A219199, A302479, A341452, A341461, A341462, A341465, A341466, A341467.

%K nonn

%O 28,5

%A _Ilya Gutkovskiy_, Feb 12 2021