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 A003072 Numbers that are the sum of 3 positive cubes. 83
 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 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 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 *) 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). Cf. A###### (x, y) = Numbers that are the sum of x nonzero y-th powers: A000404 (2, 2), A000408 (3, 2), A000414 (4, 2), A003072 (3, 3), A003325 (3, 2), 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), 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), 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), 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), 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), A003380 (2, 8), A003381 (3, 8), A003382 (4, 8), A003383 (5, 8), A003384 (6, 8), A003385 (7, 8), A003387 (9, 8), A003388 (10, 8), A003389 (11, 8), A003390 (12, 8), 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), A004802 (2, 10), A004803 (3, 10), A004804 (4, 10), A004805 (5, 10), A004806 (6, 10), A004807 (7, 10), A004808 (8, 10), A004809 (9, 10), A004810 (10, 10), A004811 (11, 10), A004812 (12, 10), A004813 (2, 11), A004814 (3, 11), A004815 (4, 11), A004816 (5, 11), A004817 (6, 11), A004818 (7, 11), A004819 (8, 11), A004820 (9, 11), A004821 (10, 11), A004822 (11, 11), A004823 (12, 11), A047700 (5, 2). Sequence in context: A063293 A270997 A024981 * A025395 A047702 A219726 Adjacent sequences:  A003069 A003070 A003071 * A003073 A003074 A003075 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Removed incorrect program. - David A. Corneth, Aug 01 2020 STATUS approved

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Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)