login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003072 Numbers that are the sum of 3 positive cubes. 41
3, 10, 17, 24, 29, 36, 43, 55, 62, 66, 73, 80, 81, 92, 99, 118, 127, 129, 134, 136, 141, 153, 155, 160, 179, 190, 192, 197, 216, 218, 225, 232, 244, 251, 253, 258, 270, 277, 281, 288, 307, 314, 342, 344, 345, 349, 352, 359, 368, 371, 375, 378, 397, 405, 408, 415, 433, 434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A119977 is a subsequence; if m is a term then there exists at least one k>0 such that m-k^3 is a term of A003325. - Reinhard Zumkeller, Jun 03 2006

A025456(a(n)) > 0. - Reinhard Zumkeller, Apr 23 2009

Davenport proved that a(n) << n^(54/47 + e) for every e > 0. - Charles R Greathouse IV, Mar 26 2012

LINKS

T. D. Noe and K. D. Bajpai, Table of n, a(n) for n = 1..12955 (first 1000 terms from T. D. Noe)

H. Davenport, Sums of three positive cubes, J. London Math. Soc., 25 (1950), 339-343. Coll. Works III p. 999.

Eric Weisstein's World of Mathematics, Cubic Number

Index entries for sequences related to sums of cubes

EXAMPLE

a(11) = 73 = 1^3 + 2^3 + 4^3, which is sum of three cubes.

a(15) = 99 = 2^3 + 3^3 + 4^3, which is sum of three cubes.

MAPLE

isA003072 := proc(n)

    local x, y, z;

    for x from 1 do

        if 3*x^3 > n then

            return false;

        end if;

        for y from x do

            if x^3+2*y^3 > n then

                break;

            end if;

            if isA000578(n-x^3-y^3) then

                return true;

            end if;

        end do:

    end do:

end proc:

for n from 1 to 1000 do

    if isA003072(n) then

        printf("%d, ", n) ;

    end if;

end do: # R. J. Mathar, Jan 23 2016

MATHEMATICA

Select[Range[435], (p = PowersRepresentations[#, 3, 3]; (Select[p, #[[1]] > 0 && #[[2]] > 0 && #[[3]] > 0 &] != {})) &] (* Jean-Fran├žois Alcover, Apr 29 2011 *)

Union[Total/@(Tuples[Range[8], 3]^3)] (* Harvey P. Dale, May 09 2012 *)

PROG

(PARI) sum(n=1, 11, x^(n^3), O(x^1400))^3

(PARI) list(lim)=my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), listput(v, k+z^3)))); Set(v) \\ Charles R Greathouse IV, Sep 14 2015

(Haskell)

a003072 n = a003072_list !! (n-1)

a003072_list = filter c3 [1..] where

   c3 x = any (== 1) $ map (a010057 . fromInteger) $

                       takeWhile (> 0) $ map (x -) $ a003325_list

-- Reinhard Zumkeller, Mar 24 2012

CROSSREFS

Subsequence of A004825.

Cf. A003325, A024981, A057904 (complement), A010057, A000578.

Sequence in context: A063293 A270997 A024981 * A025395 A047702 A219726

Adjacent sequences:  A003069 A003070 A003071 * A003073 A003074 A003075

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, David W. Wilson

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 12:26 EDT 2017. Contains 287241 sequences.