%I A000607 M0265 N0093
%S A000607 1,0,1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,17,19,23,26,30,35,40,46,52,
%T A000607 60,67,77,87,98,111,124,140,157,175,197,219,244,272,302,336,372,
%U A000607 413,456,504,557,614,677,744,819,899,987,1083,1186,1298,1420,1552
%N A000607 Number of partitions of n into prime parts.
%C A000607 a(n) gives the number of values of k for which A001414(k) = n. - Howard 
               A. Landman (howard(AT)polyamory.org), Sep 25 2001
%D A000607 R. Ayoub, An Introduction to the Analytic Theory of Numbers, Amer. Math. 
               Soc., 1963; see p. 203.
%D A000607 B. C. Berndt and B. M. Wilson, Chapter 5 of Ramanujan's second notebook, 
               pp. 49-78 of Analytic Number Theory (Philadelphia, 1980), Lect. Notes 
               Math. 899, 1981, see Entry 29.
%D A000607 D. M. Burton, Elementary Number Theory, 5th ed., McGraw-Hill, 2002.
%D A000607 L. M. Chawla and S. A. Shad, On a trio-set of partition functions and 
               their tables, J. Natural Sciences and Mathematics, 9 (1969), 87-96.
%D A000607 H. Gupta, Partitions into distinct primes, Proc. Nat. Acad. Sci. India, 
               21 (1955), 185-187.
%D A000607 O. P. Gupta and S. Luthra, Partitions into primes. Proc. Nat. Inst. Sci. 
               India. Part A. 21 (1955), 181-184.
%D A000607 R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), 
               no. 8, 697-712.
%D A000607 John F. Loase (splurge(AT)aol.com), David Lansing, Cassie Hryczaniuk, 
               Jamie Cahoon, A Variant of the Partition Function, College Mathematics 
               Journal, Vol. 36, No. 4 (Sep 2005), pp. 320-321.
%D A000607 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000607 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000607 Roger Woodford, Bounds for the Eventual Positivity of Difference Functions 
               of Partitions, Journal of Integer Sequences, Vol. 10 (2007), Article 
               07.1.3.
%H A000607 T. D. Noe, <a href="b000607.txt">Table of n, a(n) for n = 0..1000</a>
%H A000607 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               580
%H A000607 R. C. Vaughan, <a href="http://dx.doi.org/10.1007/s11139-007-9037-5">
               On the number of partitions into primes</a>, Ramanujan J. vol. 15, 
               no. 1 (2008) 109-121.
%H A000607 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimePartition.html">Link to a section of The World of Mathematics.</
               a>
%H A000607 <a href="Sindx_Go.html#Goldbach">Index entries for sequences related 
               to Goldbach conjecture</a>
%F A000607 Asymptotically a(n) ~ exp(2 Pi sqrt(n/log n) / sqrt(3)) (Ayoub).
%F A000607 a(n) = 1/n*Sum_{k=1..n} A008472(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 27 2002
%F A000607 G.f. 1/product(1-x^prime(k),k=1..infty).
%F A000607 See the partition arrays A116864 and A116865.
%e A000607 n = 10 has a(10) = 5 partitions into prime parts: 10 = 2 + 2 + 2 + 2 
               + 2 = 2 + 2 + 3 + 3 = 2 + 3 + 5 = 3 + 7 = 5 + 5. n = 15 has a(15) 
               = 12 partitions into prime parts: 15 = 2 + 2 + 2 + 2 + 2 + 2 + 3 
               = 2 + 2 + 2 + 3 + 3 + 3 = 2 + 2 + 2 + 2 + 2 + 5 = 2 + 2 + 2 + 2 + 
               7 = 2 + 2 + 3 + 3 + 5 = 2 + 3 + 5 + 5 = 2 + 3 + 3 + 7 = 2 + 2 + 11 
               = 2 + 13 = 3 + 3 + 3 + 3 + 3 = 3 + 5 + 7 = 5 + 5 + 5.
%t A000607 CoefficientList[ Series[1/Product[1 - x^Prime[i], {i, 1, 50}], {x, 0, 
               50}], x]
%o A000607 (PARI) A000607(n,m)={local(p); (m==1 | n<3) & return(1-n%2); if( m, A607[n,
               m] & return(A607[n,m]); m>(p=primepi(n)) & A607[n,m=p] & return(A607[n,
               m]), A607=matrix(n,m=primepi(n))); A607[n,m]=sum(i=0,n\p=prime(m),
               A000607(n-i*p,m-1))} - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Jan 22 2008
%Y A000607 G.f. = 1 / G.f. for A046675. Cf. A046676, A048165, A004526, A051034, 
               A000040, A001414, A000586, A000041, A070214.
%Y A000607 Cf. A046113 for the ordered (compositions) version.
%Y A000607 Cf. A112021, A056768.
%Y A000607 Row sums of array A116865.
%Y A000607 Cf. A128515.
%Y A000607 Sequence in context: A029022 A140953 A112021 this_sequence A114372 A046676 
               A003114
%Y A000607 Adjacent sequences: A000604 A000605 A000606 this_sequence A000608 A000609 
               A000610
%K A000607 easy,nonn,nice
%O A000607 0,6
%A A000607 N. J. A. Sloane (njas(AT)research.att.com).