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

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, 20, 23, 24, 26, 28, 30, 32, 35, 36, 40, 41, 46, 47, 52, 54, 58, 62, 65, 71, 73, 80, 82, 90, 93, 101, 104, 113, 117, 125, 132, 139, 148, 154, 165, 171, 183, 191

Offset: 1

Author

Reinhard Zumkeller, Aug 20 2005

Keywords

• nonn

Examples

			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 + ...
a(12) = #{3^2+3, 7+5, 7+3+2, 5+2^2+3} = 4.
		

Crossrefs

Cf. A000586, A111900, A106244, A111901.

Programs

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 */

Formula

G.f.: Product_{k>=1} (1 + x^prime(k))*(1 + x^(prime(k)^2)). - Ilya Gutkovskiy, Dec 26 2016