cp's OEIS Frontend

A000333 Number of partitions into non-integral powers.

%I A000333 M3856 N1579 #20 Feb 03 2022 22:42:15
%S A000333 1,5,15,40,98,237,534,1185,2554,5391,11117,22556,44858,88000,170107,
%T A000333 324547,611755,1140382,2103554,3842826,6955918,12483075,22220002,
%U A000333 39248230,68819781,119839422,207304370,356356801,608901907,1034452712,1747764522,2937370605,4911675955,8173032301
%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_, Jul 03 2009]
%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.
%D A000333 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000333 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%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.
%H A000333 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 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_, Jul 03 2009]
%K A000333 nonn
%O A000333 1,2
%A A000333 _N. J. A. Sloane_
%E A000333 2 more terms from _R. J. Mathar_, Jul 03 2009
%E A000333 More terms from _Sean A. Irvine_, Nov 14 2010