A003072 - OEIS

A003072

Numbers that are the sum of 3 positive cubes.

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

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

FORMULA

{n: A025456(n) >0}. - R. J. Mathar, Jun 15 2018

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 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-François Alcover, Apr 29 2011 *)

With[{upto=500}, Select[Union[Total/@Tuples[Range[Floor[Surd[upto-2, 3]]]^3, 3]], #<=upto&]] (* Harvey P. Dale, Oct 25 2021 *)

PROG

(PARI) sum(n=1, 11, x^(n^3), O(x^1400))^3 /* Then [i|i<-[1..#%], polcoef(%, i)] gives the list of powers with nonzero coefficient. - M. F. Hasler, Aug 02 2020 */

(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, A023042 (subsequence of cubes).