%I #28 Oct 02 2020 18:42:54

%S 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,

%T 204,224,257,278,320,522,595,724,776,1064,1136,1364,1634,1836,2192,

%U 2601,2761,3645,3863,4294,4549,6262,8558,9453,9964,11001,12774,13438

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

%H David A. Corneth, <a href="/A070215/b070215.txt">Table of n, a(n) for n = 1..10000</a> (first 1201 terms from Seth Troisi)

%F a(n) = A000586(prime(n)). - _R. J. Mathar_, Apr 30 2007

%e 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.

%t 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 *)

%o (Haskell)

%o a070215 = a000586 . a000040 -- _Reinhard Zumkeller_, Aug 05 2012

%Y Cf. A000586, A056768 (parts may repeat).

%K nonn

%O 1,3

%A _Lekraj Beedassy_, May 07 2002

%E More terms from _Naohiro Nomoto_ and _Don Reble_, May 11 2002

%E Offset in b-file corrected by _N. J. A. Sloane_, Aug 31 2009