Search: id:A000333
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%I A000333 M3856 N1579
%S A000333 1,5,15,40,98,237,534,1185,2554,5391,11117,22556
%N A000333 Number of partitions into non-integral powers.
%C A000333 a(n) is the number of solutions to the inequality sum_{i=1,2,3...} x_i^(1/
               2)<=n under the constraint that x_i are integers where 1<=x_1<=x_2<=x_3<=x_4<=... 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
%D A000333 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000333 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000333 B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions 
               into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 
               (1951), 207-216.
%H A000333 B. K. Agarwala, F. C. Auluck, <a href="http://dx.doi.org/10.1017/S0305004100026505">
               Statistical mechanics and partitions into non-integral powers of 
               integers</a>, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
%e A000333 a(n=3)=15 counts the solutions 1^(1/2)<=3, 1^(1/2)+1^(1/2)<=3, 1^(1/2)+1^(1/
               2)+1^(1/2)<=3, 1^(1/2)+2^(1/2)<=3, 1^(1/2)+3^(1/2)<=3, 1^(1/2)+4^(1/
               2)<=3, 2^(1/2)<=3, 2^(1/2)+2^(1/2)<=3, 3^(1/2)<=3, 4^(1/2)<=3,.., 
               8^(1/2)<=3 and 9^(1/2)<=3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jul 03 2009]
%Y A000333 Sequence in context: A132985 A022570 A152881 this_sequence A054888 A038066 
               A113861
%Y A000333 Adjacent sequences: A000330 A000331 A000332 this_sequence A000334 A000335 
               A000336
%K A000333 nonn,easy
%O A000333 1,2
%A A000333 N. J. A. Sloane (njas(AT)research.att.com).
%E A000333 2 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 
               2009

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