A341462 - OEIS

%I #12 Nov 07 2021 11:33:57

%S 1,1,1,1,2,2,3,3,5,5,7,6,10,9,13,12,17,17,21,21,28,28,34,33,42,43,51,

%T 53,61,63,73,76,87,91,102,104,119,123,137,143,157,164,179,187,205,215,

%U 232,239,262,272,294,309,327,341,365,381,406,427,448,465

%N Number of partitions of n into 4 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, 4):

%p seq(a(n), n=19..78);  # _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, 4];

%t Table[a[n], {n, 19, 78}] (* _Jean-François Alcover_, Jul 13 2021, after _Alois P. Heinz_ *)

%t Table[Length[Select[IntegerPartitions[n,{4}],Length[#]==Length[ Union[ #]] && NoneTrue[#,PrimeQ]&]],{n,19,80}] (* _Harvey P. Dale_, Nov 07 2021 *)

%Y Cf. A005171, A018252, A096258, A219198, A302479, A341451, A341461, A341464, A341465, A341466, A341467.

%K nonn

%O 19,5

%A _Ilya Gutkovskiy_, Feb 12 2021