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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000339 Number of partitions into non-integral powers. (Formerly M3879 N1590) 2
 1, 5, 18, 45, 100, 185, 323, 522, 804, 1180, 1687, 2322, 3139, 4146, 5377, 6859, 8645, 10733, 13203, 16058, 19356, 23132, 27460, 32330, 37846, 44031, 50954, 58637, 67203, 76613, 87021, 98443, 110951, 124616, 139526, 155681, 173246, 192243 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(n) counts the solutions to the inequality x_1^(1/2)+x_2^(1/2)<=n for any two integers 1<=x_1<=x_2. - R. J. Mathar, Jul 03 2009 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216. 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. [Annotated scanned copy] MAPLE A000339 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to n^2 do x2 := (n-x1^(1/2))^2 ; if floor(x2) >= x1 then a := a+floor(x2-x1+1) ; fi; od: a ; end: for n from 2 to 80 do printf("%d, \n", A000339(n)) ; od: # R. J. Mathar, Sep 29 2009 MATHEMATICA A000339[n_] := Module[{a, x1, x2}, a = 0; For[x1 = 1 , x1 <= n^2 , x1++, x2 = (n-x1^(1/2))^2; If[Floor[x2] >= x1, a = a+Floor[x2-x1+1]]]; a]; Reap[ For[n = 2, n <= 80, n++, Print[an = A000339[n]]; Sow[an]]][[2, 1]] (* Jean-François Alcover, Feb 07 2016, after R. J. Mathar *) CROSSREFS Sequence in context: A321049 A007237 A327842 * A270944 A272457 A081435 Adjacent sequences:  A000336 A000337 A000338 * A000340 A000341 A000342 KEYWORD nonn AUTHOR EXTENSIONS More terms from R. J. Mathar, Sep 29 2009 STATUS approved

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.

Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)