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
Offset: 1
Examples
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.
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
Crossrefs
Subsequence of A004825.
Cf. A###### (x, y) = Numbers that are the sum of x nonzero y-th powers:
- cubes: A003325 (2, 3), A003072 (3, 3), A003327 (4, 3), A003328 (5, 3), A003329 (6, 3), A003330 (7, 3), A003331 (8, 3), A003332 (9, 3), A003333 (10, 3), A003334 (11, 3), A003335 (12, 3);
- fourth powers: A003336 (2, 4), A003337 (3, 4), A003338 (4, 4), A003339 (5, 4), A003340 (6, 4), A003341 (7, 4), A003342 (8, 4), A003343 (9, 4), A003344 (10, 4), A003345 (11, 4), A003346 (12, 4);
- fifth powers: A003347 (2, 5), A003348 (3, 5), A003349 (4, 5), A003350 (5, 5), A003351 (6, 5), A003352 (7, 5), A003353 (8, 5), A003354 (9, 5), A003355 (10, 5), A003356 (11, 5), A003357 (12, 5);
- sixth powers: A003358 (2, 6), A003359 (3, 6), A003360 (4, 6), A003361 (5, 6), A003362 (6, 6), A003363 (7, 6), A003364 (8, 6), A003365 (9, 6), A003366 (10, 6), A003367 (11, 6), A003368 (12, 6);
- seventh powers: A003369 (2, 7), A003370 (3, 7), A003371 (4, 7), A003372 (5, 7), A003373 (6, 7), A003374 (7, 7), A003375 (8, 7), A003376 (9, 7), A003377 (10, 7), A003378 (11, 7), A003379 (12, 7);
- eighth powers: A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003386 (8, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8);
- ninth powers: A003391 (2, 9), A003392 (3, 9), A003393 (4, 9), A003394 (5, 9), A003395 (6, 9), A003396 (7, 9), A003397 (8, 9), A003398 (9, 9), A003399 (10, 9), A004800 (11, 9), A004801 (12, 9);
Programs
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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 -
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
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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 *) -
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 */
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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
Formula
{n: A025456(n) >0}. - R. J. Mathar, Jun 15 2018
Extensions
Incorrect program removed by David A. Corneth, Aug 01 2020
Comments