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A000327 Number of partitions into non-integral powers.
(Formerly M3819 N1563)
2
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

Table of n, a(n) for n=3..47.

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

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-Fran├žois Alcover, Feb 07 2016, after R. J. Mathar *)

CROSSREFS

Sequence in context: A054307 A172295 A126573 * A220425 A130624 A066869

Adjacent sequences:  A000324 A000325 A000326 * A000328 A000329 A000330

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. J. Mathar, Sep 29 2009

STATUS

approved

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.