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URL: https://oeis.org/A259195

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A259195
Number of partitions of n into five primes.
18
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 5, 4, 6, 6, 7, 6, 10, 7, 11, 9, 12, 11, 17, 11, 18, 13, 20, 14, 24, 15, 27, 18, 29, 21, 35, 19, 38, 24, 41, 26, 47, 26, 53, 30, 54, 34, 64, 33, 70, 38, 73, 41, 81, 41, 89, 45, 92, 50, 103, 47, 112, 56, 117, 61, 127, 57
OFFSET
0,14
LINKS
David A. Corneth, Table of n, a(n) for n = 0..10000 (first 5001 terms from Doug Bell)
Sean A. Irvine, Java program (github)
FORMULA
a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(i) * c(j) * c(k) * c(l) * c(n-i-j-k-l), where c = A010051. - Wesley Ivan Hurt, Apr 17 2019
a(n) = [x^n y^5] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019
EXAMPLE
a(17) = 3 because 17 can be written as the sum of five primes in exactly three ways: 2+2+3+3+7, 2+2+3+5+5, and 3+3+3+3+5.
MATHEMATICA
Array[Count[IntegerPartitions[#, {5}], _?(AllTrue[#, PrimeQ] &)] &, 71] (* Michael De Vlieger, Apr 21 2019 *)
PROG
(PARI) a(n) = {nb = 0; forpart(p=n, if (#p && (#select(x->isprime(x), Vec(p)) == #p), nb+=1), , [5, 5]); nb; } \\ Michel Marcus, Jun 21 2015
(Magma) [0] cat [#RestrictedPartitions(n, 5, {p:p in PrimesUpTo(n)}):n in [1..70]]; // Marius A. Burtea, May 09 2019
CROSSREFS
Column k=5 of A117278.
Number of partitions of n into r primes for r = 1..10: A010051, A061358, A068307, A259194, this sequence, A259196, A259197, A259198, A259200, A259201.
Cf. A000040.
Sequence in context: A167227 A048280 A024695 * A143997 A160903 A124229
KEYWORD
nonn,easy
AUTHOR
Doug Bell, Jun 20 2015
EXTENSIONS
More terms from David A. Corneth, Sep 06 2020
STATUS
approved