%I M1830 N0726 #16 Jun 27 2015 17:50:28

%S 1,2,8,19,41,78,134,218,339,506,730,1023,1397,1884,2477,3218,4118,

%T 5192,6486,8010,9795,11888,14302,17066,20256,23889,27999,32637,37863,

%U 43695,50218,57495,65545,74431,84257,95030,106840,119799,133941,149311,166071

%N Number of partitions into non-integral powers.

%C a(n) counts the solutions to the inequality x_1^(2/3)+x_2^(2/3)+x_3^(2/3)<=n for any three integers 1<=x_1<=x_2<=x_3. - _R. J. Mathar_, Jul 03 2009

%D 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 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 B. K. Agarwala and F. C. Auluck, <a href="/A000093/a000093.pdf">Statistical mechanics and partitions into non-integral powers of integers</a>, Proc. Camb. Phil. Soc., 47 (1951), 207-216. [Annotated scanned copy]

%Y Cf. A000148, A000160, A000234. - _R. J. Mathar_, Jul 03 2009

%K nonn

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Oct 11 2009