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 A259200 Number of partitions of n into nine primes. 22
 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 7, 9, 10, 11, 12, 16, 16, 20, 21, 24, 26, 33, 31, 39, 39, 47, 46, 59, 53, 69, 65, 80, 77, 98, 85, 114, 104, 131, 118, 154, 133, 179, 155, 200, 177, 236, 196, 268, 227, 300, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 18,4 LINKS Robert Israel, Table of n, a(n) for n = 18..10000 FORMULA a(n) = [x^n y^9] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019 a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} A010051(q) * A010051(p) * A010051(o) * A010051(m) * A010051(l) * A010051(k) * A010051(j) * A010051(i) * A010051(n-i-j-k-l-m-o-p-q). - Wesley Ivan Hurt, Jul 13 2019 EXAMPLE a(23) = 3 because there are 3 partitions of 23 into nine primes: [2,2,2,2,2,2,2,2,7], [2,2,2,2,2,2,3,3,5] and [2,2,2,2,3,3,3,3,3]. MAPLE N:= 100: # to get a(0) to a(N) Primes:= select(isprime, [\$1..N]): np:= nops(Primes): for j from 0 to np do g[0, j]:= 1 od: for n from 1 to 9 do   g[n, 0]:= 0:   for j from 1 to np do      g[n, j]:= convert(series(add(g[k, j-1]           *x^((n-k)*Primes[j]), k=0..n), x, N+1), polynom)   od od: seq(coeff(g[9, np], x, i), i=18..N) # Robert Israel, Jun 21 2015 MATHEMATICA Table[Length[Select[IntegerPartitions[n], Length[#]==9&&AllTrue[ #, PrimeQ]&]], {n, 18, 70}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 31 2016 *) PROG (PARI) a(n) = {nb = 0; forpart(p=n, if (#p && (#select(x->isprime(x), Vec(p)) == #p), nb+=1), , [9, 9]); nb; } \\ Michel Marcus, Jun 21 2015 (MAGMA) [#RestrictedPartitions(k, 9, Set(PrimesUpTo(1000))):k in [18..70]] ; // Marius A. Burtea, Jul 13 2019 CROSSREFS Column k=9 of A117278. Number of partitions of n into r primes for r = 1..10: A010051, A061358, A068307, A259194, A259195, A259196, A259197, A259198, this sequence, A259201. Cf. A000040. Sequence in context: A029042 A320470 A320382 * A153155 A225085 A134310 Adjacent sequences:  A259197 A259198 A259199 * A259201 A259202 A259203 KEYWORD nonn,easy AUTHOR Doug Bell, Jun 20 2015 STATUS approved

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Last modified June 17 18:39 EDT 2021. Contains 345085 sequences. (Running on oeis4.)