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A111902
Number of partitions of n into distinct parts that are primes or squares of primes.
3
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
1,6
FORMULA
G.f.: Product_{k>=1} (1 + x^prime(k))*(1 + x^(prime(k)^2)). - Ilya Gutkovskiy, Dec 26 2016
EXAMPLE
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.
PROG
(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 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 20 2005
STATUS
approved