login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000333 Number of partitions into non-integral powers.
(Formerly M3856 N1579)
0

%I M3856 N1579

%S 1,5,15,40,98,237,534,1185,2554,5391,11117,22556,44858,88000,170107,

%T 324547,611755,1140382,2103554,3842826,6955918,12483075,22220002,

%U 39248230,68819781,119839422,207304370,356356801,608901907,1034452712,1747764522,2937370605,4911675955,8173032301

%N Number of partitions into non-integral powers.

%C 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 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 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 nonn

%O 1,2

%A _N. J. A. Sloane_.

%E 2 more terms from _R. J. Mathar_, Jul 03 2009

%E More terms from _Sean A. Irvine_, Nov 14 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)