A341948 - OEIS

%I #12 Feb 15 2022 07:46:45

%S 1,1,2,2,4,4,6,5,8,6,10,7,12,9,15,10,18,12,21,14,25,15,29,18,33,21,37,

%T 20,41,23,46,26,51,27,58,31,63,34,68,33,77,39,83,42,90,43,101,48,107,

%U 53,116,52,128,58,134,61,142,61,157,68,165,73,176,73,194,82,201,84,211

%N Number of partitions of n into 5 primes (counting 1 as a prime).

%H Alois P. Heinz, <a href="/A341948/b341948.txt">Table of n, a(n) for n = 5..10000</a>

%p b:= proc(n, i) option remember; series(`if`(n=0, 1,

%p      `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(

%p      `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 6)

%p     end:

%p a:= n-> coeff(b(n, numtheory[pi](n)), x, 5):

%p seq(a(n), n=5..73);  # _Alois P. Heinz_, Feb 24 2021

%t b[n_, i_] := b[n, i] = Series[If[n == 0, 1,

%t      If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][

%t      If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 6}];

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

%t Table[a[n], {n, 5, 73}] (* _Jean-François Alcover_, Feb 15 2022, after _Alois P. Heinz_ *)

%Y Cf. A008578, A034891, A259195, A341945, A341946, A341947, A341949, A341950, A341951.

%K nonn

%O 5,3

%A _Ilya Gutkovskiy_, Feb 24 2021