A070215 Number of ways to write the n-th prime as a sum of distinct primes.

1, 1, 2, 2, 1, 2, 2, 3, 5, 7, 9, 11, 14, 15, 19, 26, 35, 39, 50, 61, 67, 87, 102, 130, 178, 204, 224, 257, 278, 320, 522, 595, 724, 776, 1064, 1136, 1364, 1634, 1836, 2192, 2601, 2761, 3645, 3863, 4294, 4549, 6262, 8558, 9453, 9964, 11001, 12774, 13438

Offset

1,3

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1201 terms from Seth Troisi)

Formula

a(n) = A000586(prime(n)). - R. J. Mathar, Apr 30 2007

Example

With the 10th prime 29, for instance, we have a(10)=7 distinct-prime partitions, viz. 29 = 2 + 3 + 7 + 17 = 2 + 3 + 5 + 19 = 2 + 3 + 11 + 13 = 3 + 7 + 19 = 5 + 7 + 17 = 5 + 11 + 13.

Mathematica

nn = PrimePi[300]; t = CoefficientList[Series[Product[(1 + x^Prime[k]), {k, nn}], {x, 0, Prime[nn]}], x]; t[[1 + Prime[Range[nn]]]] (* T. D. Noe, Nov 13 2013 *)

Prog

(Haskell)
a070215 = a000586 . a000040  -- Reinhard Zumkeller, Aug 05 2012

Crossrefs

Cf. A000586, A056768 (parts may repeat).

Sequence in context: A112175 A112206 A038541 * A071457 A227782 A255771

Adjacent sequences: A070212 A070213 A070214 * A070216 A070217 A070218

Keyword

nonn

Author

Lekraj Beedassy, May 07 2002

Extensions

More terms from Naohiro Nomoto and Don Reble, May 11 2002

Offset in b-file corrected by N. J. A. Sloane, Aug 31 2009

Status

approved