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 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: A101105 A037140 A007237 * 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

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Last modified November 21 16:08 EST 2017. Contains 295003 sequences.