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 A000327 Number of partitions into non-integral powers. (Formerly M3819 N1563) 3
 1, 5, 12, 23, 39, 62, 91, 127, 171, 228, 294, 370, 461, 561, 677, 811, 955, 1121, 1303, 1499, 1719, 1960, 2218, 2499, 2806, 3131, 3485, 3868, 4274, 4706, 5166, 5658, 6175, 6725, 7309, 7923, 8572, 9256, 9972, 10728, 11521, 12349, 13218, 14126, 15072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS a(n) counts the solutions to the inequality x_1^(2/3) + x_2^(2/3) <= n for any two distinct 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 Seth A. Troisi, Table of n, a(n) for n = 3..1000 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. 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] FORMULA a(n) = A000148(n) - floor((n/2)^(3/2)). - Seth A. Troisi, May 25 2022 MAPLE A000327 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to floor(n^(3/2)) do x2 := (n-x1^(2/3))^(3/2) ; if floor(x2) >= x1+1 then a := a+floor(x2-x1) ; fi; od: a ; end: seq(A000327(n), n=3..80) ; # R. J. Mathar, Sep 29 2009 MATHEMATICA A000327[n_] := Module[{a, x1, x2 }, a = 0; For[x1 = 1, x1 <= Floor[ n^(3/2)], x1++, x2 = (n - x1^(2/3))^(3/2); If[Floor[x2] >= x1+1, a = a + Floor[x2 - x1]]]; a ]; Table[A000327[n], {n, 3, 80}] (* Jean-François Alcover, Feb 07 2016, after R. J. Mathar *) A000327[n_] := Sum[Min[x1 - 1, Floor[(n - x1^(2/3))^(3/2)]], {x1, 2, Floor[n^(3/2)]}]; Table[A000327[n], {n, 3, 80}] (* Seth A. Troisi, May 25 2022 *) CROSSREFS Cf. A000148, A000158, A000160. Sequence in context: A332569 A126573 A341209 * A220425 A130624 A344846 Adjacent sequences: A000324 A000325 A000326 * A000328 A000329 A000330 KEYWORD nonn AUTHOR EXTENSIONS More terms from R. J. Mathar, Sep 29 2009 STATUS approved

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Last modified December 5 18:02 EST 2022. Contains 358588 sequences. (Running on oeis4.)