%I A000586 M0022 N0004
%S A000586 1,0,1,1,0,2,0,2,1,1,2,1,2,2,2,2,3,2,4,3,4,4,4,5,5,5,6,5,6,7,6,9,7,9,9,
               9,
%T A000586 11,11,11,13,12,14,15,15,17,16,18,19,20,21,23,22,25,26,27,30,29,32,32,
               35,
%U A000586 37,39,40,42,44,45,50,50,53,55,57,61,64,67,70,71,76,78,83,87,89,93,96
%N A000586 Number of partitions of n into distinct primes.
%D A000586 H. Gupta, Partitions into distinct primes, Proc. Nat. Acad. Sci. India, 
               21 (1955), 185-187.
%D A000586 H. Gupta, Certain averages connected with partitions. Res. Bull. Panjab 
               Univ. no. 124 1957 427-430.
%D A000586 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000586 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000586 T. D. Noe, <a href="b000586.txt">Table of n, a(n) for n = 0..1000</a>
%F A000586 G.f.: Product_{k=1..inf} (1+x^prime(k)).
%e A000586 n=16 has a(16)=3 partitions into distinct prime parts: 16 = 2+3+11 = 
               3+13 = 5+11.
%t A000586 CoefficientList[Series[Product[(1+x^Prime[k]), {k, 24}], {x, 0, Prime[24]}], 
               x]
%Y A000586 Cf. A000041, A070215, A000607.
%Y A000586 Cf. A112022.
%Y A000586 Sequence in context: A035226 A126043 A112022 this_sequence A029399 A046069 
               A055651
%Y A000586 Adjacent sequences: A000583 A000584 A000585 this_sequence A000587 A000588 
               A000589
%K A000586 nonn,nice,easy
%O A000586 0,6
%A A000586 N. J. A. Sloane (njas(AT)research.att.com).