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 A056768 Number of partitions of the n-th prime into prime parts. 17
 1, 1, 2, 3, 6, 9, 17, 23, 40, 87, 111, 219, 336, 413, 614, 1083, 1850, 2198, 3630, 5007, 5861, 9282, 12488, 19232, 33439, 43709, 49871, 64671, 73506, 94625, 221265, 279516, 394170, 441250, 766262, 853692, 1175344, 1608014, 1975108, 2675925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..4000 FORMULA a(n) = A000607(prime(n)). a(n) = A168470(n) + 1. - Alonso del Arte, Feb 15 2014, restating the corresponding formula given by R. J. Mathar for A168470. a(n) = [x^prime(n)] Product_{k>=1} 1/(1 - x^prime(k)). - Ilya Gutkovskiy, Jun 05 2017 EXAMPLE a(4) = 3 because the 4th prime is 7 which can be partitioned using primes in 3 ways: 7, 5 + 2, or 3 + 2 + 2. In connection with the 6th prime 13, for instance, we have the a(6) = 9 prime partitions: 13 = 2 + 2 + 2 + 2 + 2 + 3 = 2 + 2 + 2 + 2 + 5 = 2 + 2 + 2 + 7 = 2 + 2 + 3 + 3 + 3 = 2 + 3 + 3 + 5 = 2 + 11 = 3 + 3 + 7 = 3 + 5 + 5. MAPLE b:= proc(n, i) option remember; `if`(n=0 or i=2        and n::even, 1, `if`(i=2 or n=1, 0,        b(n, prevprime(i)))+`if`(i>n, 0, b(n-i, i)))     end: a:= n-> b(ithprime(n)\$2): seq(a(n), n=1..50);  # Alois P. Heinz, Sep 15 2016 MATHEMATICA Table[Count[IntegerPartitions[n], _?(AllTrue[#, PrimeQ]&)], {n, Prime[ Range[ 40]]}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 07 2015 *) n=40; ser=Product[1/(1-x^Prime[i]), {i, 1, n}]; Table[SeriesCoefficient[ser, {x, 0, Prime[i]}], {i, 1, n}] (* Gus Wiseman, Sep 14 2016 *) PROG (Haskell) a056768 = a000607 . a000040  -- Reinhard Zumkeller, Aug 05 2012 CROSSREFS Cf. A000041, A000607, A100118, A276687. Sequence in context: A018721 A018384 A282842 * A029511 A320271 A056532 Adjacent sequences:  A056765 A056766 A056767 * A056769 A056770 A056771 KEYWORD nonn AUTHOR Brian Galebach, Aug 16 2000 EXTENSIONS More terms from James A. Sellers, Aug 25 2000 STATUS approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)