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

Author

Lekraj Beedassy, May 07 2002

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000586, A056768 (parts may repeat).

Programs

Haskell

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

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 *)

Formula

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

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