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%I A070215 #28 Oct 02 2020 18:42:54
%S A070215 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 A070215 204,224,257,278,320,522,595,724,776,1064,1136,1364,1634,1836,2192,
%U A070215 2601,2761,3645,3863,4294,4549,6262,8558,9453,9964,11001,12774,13438
%N A070215 Number of ways to write the n-th prime as a sum of distinct primes.
%H A070215 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 A070215 a(n) = A000586(prime(n)). - _R. J. Mathar_, Apr 30 2007
%e A070215 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 A070215 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 A070215 (Haskell)
%o A070215 a070215 = a000586 . a000040  -- _Reinhard Zumkeller_, Aug 05 2012
%Y A070215 Cf. A000586, A056768 (parts may repeat).
%K A070215 nonn
%O A070215 1,3
%A A070215 _Lekraj Beedassy_, May 07 2002
%E A070215 More terms from _Naohiro Nomoto_ and _Don Reble_, May 11 2002
%E A070215 Offset in b-file corrected by _N. J. A. Sloane_, Aug 31 2009

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