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%I M1743 N0691 #31 Jul 01 2022 22:17:53
%S 1,2,7,15,28,45,70,100,138,183,242,310,388,481,583,701,838,984,1152,
%T 1337,1535,1757,2001,2262,2545,2855,3183,3540,3926,4335,4770,5233,
%U 5728,6248,6801,7388,8005,8658,9345,10064,10824,11620,12452,13324,14236
%N Number of partitions into non-integral powers.
%C a(n) is the number of solutions to the inequality x_1^(2/3) + x_2^(2/3) <= n where 1 <= x_1 <= x_2 are any two integers. If the number of terms in the sum is not restricted to 2, we get A000234. - _R. J. Mathar_, Jul 03 2009
%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 Seth A. Troisi, <a href="/A000148/b000148.txt">Table of n, a(n) for n = 2..1000</a>
%H B. K. Agarwala and 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]
%t A000148[n_] := Sum[Min[xi, Floor[(n - xi^(2/3))^(3/2)]], {xi, 1, Floor[n^(3/2)]}];
%t Table[A000148[n], {n, 2, 100}] (* _Seth A. Troisi_, May 25 2022 *)
%Y Cf. A000158, A000160, A000327.
%K nonn
%O 2,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Oct 08 2009
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