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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..67.

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

Cf. A000586, A111900, A106244, A111901.

Sequence in context: A087145 A117172 A029207 * A316211 A329480 A277895

Adjacent sequences:  A111899 A111900 A111901 * A111903 A111904 A111905

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 20 2005

STATUS

approved

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)