%I A000135 M1595 N0622
%S A000135 1,2,6,13,24,42,73,125,204,324,511,801,1228,1856,2780,4135,6084,8873,
%T A000135 12847,18481,26416,37473,52871,74216,103596,143841,198839,273654,374987,
%U A000135 511735,695559,941932,1271139,1709474,2291195,3061385,4078152,5416322
%N A000135 Number of partitions into non-integral powers.
%C A000135 a(n) counts the solutions to the inequality sum_{i=1,2,..} x_i^(2/3)<=n 
               for any number of distinct integers 1<=x_1<x_2<x_3<x_4<... - R. J. 
               Mathar, Jul 03 2009
%D A000135 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.
%D A000135 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000135 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000135 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.
%H A000135 Sean A. Irvine, <a href="a000135.txt">Tentative values of first 55 terms</
               a>
%e A000135 For n=3, the 6 solutions are (i) 1^(2/3)<=3. (ii) 1^(2/3)+2^(2/3)<=3. 
               (iii) 2^(2/3)<=3. (iv) 3^(2/3)<=3. (v) 4^(2/3)<=3. (vi) 5^(2/3)<=3. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
%Y A000135 Cf. A000148, A000158, A000160.
%Y A000135 Sequence in context: A143689 A011891 A003600 this_sequence A065220 A048094 
               A031872
%Y A000135 Adjacent sequences: A000132 A000133 A000134 this_sequence A000136 A000137 
               A000138
%K A000135 nonn
%O A000135 1,2
%A A000135 N. J. A. Sloane (njas(AT)research.att.com).
%E A000135 8 more terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 
               2009
%E A000135 20 more terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Sep 28 2009