cp's OEIS Frontend

A111902 Number of partitions of n into distinct parts that are primes or squares of primes.

%I A111902 #9 Dec 27 2016 02:47:57
%S A111902 1,0,1,1,1,2,1,3,1,4,2,4,4,4,6,4,8,5,9,7,10,9,11,12,12,15,14,17,17,20,
%T A111902 20,23,24,26,28,30,32,35,36,40,41,46,47,52,54,58,62,65,71,73,80,82,90,
%U A111902 93,101,104,113,117,125,132,139,148,154,165,171,183,191
%N A111902 Number of partitions of n into distinct parts that are primes or squares of primes.
%F A111902 G.f.: Product_{k>=1} (1 + x^prime(k))*(1 + x^(prime(k)^2)). - _Ilya Gutkovskiy_, Dec 26 2016
%e A111902 G.f. = 1 + x^2 + x^3 + x^4 + 2*x^5 + x^6 + 3*x^7 + x^8 + 4*x^9 + 2*x^10 + ...
%e A111902 a(12) = #{3^2+3, 7+5, 7+3+2, 5+2^2+3} = 4.
%o A111902 (PARI) {a(n) = if(n < 0, 0, polcoeff( prod(k=1, primepi(n), (1 + x^prime(k)^2 + x*O(x^n)) * (1 + x^prime(k))), n))}; /* _Michael Somos_, Dec 26 2016 */
%Y A111902 Cf. A000586, A111900, A106244, A111901.
%K A111902 nonn
%O A111902 1,6
%A A111902 _Reinhard Zumkeller_, Aug 20 2005