cp's OEIS Frontend

A038499 Number of partitions of n into a prime number of parts.

%I A038499 #36 Jan 02 2017 02:36:46
%S A038499 1,0,1,2,3,5,7,10,13,18,23,31,39,52,65,84,104,134,165,210,258,324,397,
%T A038499 495,603,747,908,1115,1351,1652,1993,2425,2918,3531,4237,5106,6105,
%U A038499 7330,8741,10449,12425,14804,17549,20839,24637,29155,34377,40559,47688,56100
%N A038499 Number of partitions of n into a prime number of parts.
%C A038499 Also, number of partitions of n whose largest part is a prime. E.g., for a(7) = 10 we have 6+1 = 5+2 = 4+3 = 5+1+1 = 4+2+1 = 3+3+1 = 3+2+2 = 3+1+1+1+1 = 2+2+1+1+1 = 1+1+1+1+1+1+1 and 7 = 5+2 = 5+1+1 = 3+3+1 = 3+2+2 = 3+2+1+1 = 3+1+1+1+1 = 2+2+2+1 = 2+2+1+1+1 = 2+1+1+1+1+1. - _Jon Perry_ Jul 06 2004
%H A038499 Alois P. Heinz, <a href="/A038499/b038499.txt">Table of n, a(n) for n = 0..10000</a>
%F A038499 G.f.: Sum_{n>=1}(x^prime(n)/Product_{i=1..prime(n)}(1-x^i)). - _Vladeta Jovovic_, Dec 25 2003
%p A038499 with(numtheory):
%p A038499 b:= proc(n, i) option remember; `if`(n<0, 0,
%p A038499       `if`(n=0 or i=1, 1, `if`(i<1, 0, b(n, i-1)+
%p A038499       `if`(i>n, 0, b(n-i, i)))))
%p A038499     end:
%p A038499 a:= n-> `if`(n=0, 1, add((p-> b(n-p, p)
%p A038499            )(ithprime(i)), i=1..pi(n))):
%p A038499 seq(a(n), n=0..60);  # _Alois P. Heinz_, Sep 24 2015
%t A038499 nn=50;Table[CoefficientList[Series[x^p Product[1/(1-x^i),{i,1,p}],{x,0,nn}],x],{p,Table[Prime[m],{m,1,PrimePi[nn]}]}]//Total  (* _Geoffrey Critzer_, Mar 10 2013 *)
%Y A038499 Cf. A027187, A027193.
%K A038499 nonn
%O A038499 0,4
%A A038499 _Christian G. Bower_, Feb 15 1999