%I M3439 N1395 #20 Jun 27 2015 17:55:46

%S 1,4,12,30,70,159,339,706,1436,2853,5551,10622,19975,37043,67811,

%T 122561,219090,387578,678977,1178769,2029115,3465056,5872648,9882301,

%U 16517284,27430358,45275673,74297072,121245153,196810381,317850809,510830685,817139589,1301251186,2063204707,3257690903,5123047561

%N Number of partitions into non-integral powers.

%C a(n) is the number of solutions to the inequality sum_{i=1,2,..} x_i^(1/2)<=n for unknowns 1<=x_1<x_2<x_3<x_4<.... - _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]

%e The 12 solutions for n=3 are 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, 3^(1/2)<=3,...,8^(1/2)<=3 and 9^(1/2)<=3. - _R. J. Mathar_, Jul 03 2009

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E 3 more terms from _R. J. Mathar_, Jul 03 2009

%E More terms from _Sean A. Irvine_, Nov 11 2010