cp's OEIS Frontend

A341975 Number of partitions of n into 4 distinct primes (counting 1 as a prime).

%I A341975 #11 Jul 13 2021 02:51:40
%S A341975 1,0,1,0,1,1,2,0,2,1,3,2,4,2,4,3,5,4,5,3,5,6,7,6,6,7,8,9,9,10,7,10,9,
%T A341975 12,10,12,9,15,12,16,13,18,12,20,14,22,16,23,13,27,16,29,19,30,14,33,
%U A341975 19,36,21,35,15,43,23,43,23,43,18,52,26,51,26,52,21,64,29,58,28,64
%N A341975 Number of partitions of n into 4 distinct primes (counting 1 as a prime).
%p A341975 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A341975      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
%p A341975      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 5)
%p A341975     end:
%p A341975 a:= n-> coeff(b(n, numtheory[pi](n)), x, 4):
%p A341975 seq(a(n), n=11..88);  # _Alois P. Heinz_, Feb 24 2021
%t A341975 b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
%t A341975      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][
%t A341975      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 5}];
%t A341975 a[n_] := Coefficient[b[n, PrimePi[n]], x, 4];
%t A341975 Table[a[n], {n, 11, 100}] (* _Jean-François Alcover_, Jul 13 2021, after _Alois P. Heinz_ *)
%Y A341975 Cf. A008578, A036497, A219198, A341947, A341973, A341974, A341976, A341977.
%K A341975 nonn
%O A341975 11,7
%A A341975 _Ilya Gutkovskiy_, Feb 24 2021