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 A259198 Number of partitions of n into eight primes. 17
 1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 9, 12, 14, 16, 16, 21, 19, 26, 26, 31, 30, 39, 34, 46, 43, 53, 48, 65, 56, 77, 66, 85, 77, 104, 84, 118, 99, 133, 112, 155, 123, 177, 143, 196, 162, 227, 174, 256, 200, 282, 220, 318, 241, 360, 270, 389, 300, 442, 322 (list; graph; refs; listen; history; text; internal format)
 OFFSET 16,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 16..10000 FORMULA a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(p) * A010051(n-i-j-k-l-m-o-p). - Wesley Ivan Hurt, Apr 17 2019 a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019 a(n) = A326455(n)/n for n > 0. - Wesley Ivan Hurt, Jul 06 2019 EXAMPLE a(20) = 2 because there are 2 partitions of 20 into eight primes: [2,2,2,2,2,2,3,5] and [2,2,2,2,3,3,3,3]. CROSSREFS Column k=8 of A117278. Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, A259196, A259197, this sequence, A259200, A259201. Cf. A000040. Sequence in context: A008672 A097923 A027582 * A011880 A029044 A029043 Adjacent sequences:  A259195 A259196 A259197 * A259199 A259200 A259201 KEYWORD nonn,easy AUTHOR Doug Bell, Jun 20 2015 STATUS approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)