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 A004825 Numbers that are the sum of at most 3 positive cubes. 16
 0, 1, 2, 3, 8, 9, 10, 16, 17, 24, 27, 28, 29, 35, 36, 43, 54, 55, 62, 64, 65, 66, 72, 73, 80, 81, 91, 92, 99, 118, 125, 126, 127, 128, 129, 133, 134, 136, 141, 152, 153, 155, 160, 179, 189, 190, 192, 197, 216, 217, 218, 224, 225, 232, 243, 244, 250, 251, 253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Or: numbers which are the sum of 3 (not necessarily distinct) nonnegative cubes. - R. J. Mathar, Sep 09 2015 Deshouillers, Hennecart, & Landreau conjecture that this sequence has density 0.0999425... = lim_K sum_{k=1..K} exp(c*rho(k,K)/K^2)/K where c = -gamma(4/3)^3/6 = -0.1186788..., K takes increasing values in A003418 (or, equivalently, A051451), and rho(k0,K) is the number of triples 1 <= k1,k2,k3 <= K such that k0 = k1^3 + k2^3 + k3^3 mod K. - Charles R Greathouse IV, Sep 16 2016 LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) Jean-Marc Deshouillers, François Hennecart, and Bernard Landreau, On the density of sums of three cubes, ANTS-VII (2006), pp. 141-155. MAPLE isA004825 := proc(n)     local x, y, zc ;     for x from 0 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;             else                 zc := n-x^3-y^3 ;                 if zc >= y^3 and isA000578(zc) then                     return true;                 end if;             end if;         end do:     end do: end proc: A004825 := proc(n)     option remember;     local a;     if n = 1 then         0;     else         for a from procname(n-1)+1 do             if isA004825(a) then                 return a;             end if;         end do:     end if; end proc: seq(A004825(n), n=1..100) ; # R. J. Mathar, Sep 09 2015 # second Maple program: b:= proc(n, i, t) option remember; n=0 or i>0 and t>0       and (b(n, i-1, t) or i^3<=n and b(n-i^3, i, t-1))     end: a:= proc(n) option remember; local k;       for k from 1+ `if`(n=1, -1, a(n-1))       while not b(k, iroot(k, 3), 3) do od; k     end: seq(a(n), n=1..100);  # Alois P. Heinz, Sep 16 2016 MATHEMATICA q=7; imax=q^3; Select[Union[Flatten[Table[x^3+y^3+z^3, {x, 0, q}, {y, x, q}, {z, y, q}]]], #<=imax&] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *) PROG (PARI) list(lim)=my(v=List(), k, t); for(x=0, sqrtnint(lim\=1, 3), for(y=0, min(sqrtnint(lim-x^3, 3), x), k=x^3+y^3; for(z=0, min(sqrtnint(lim-k, 3), y), listput(v, k+z^3)))); Set(v) \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS A003072 is a subsequence. Cf. A004999. Column k=3 of A336820. Sequence in context: A169868 A191159 A047360 * A272830 A028821 A337261 Adjacent sequences:  A004822 A004823 A004824 * A004826 A004827 A004828 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 20 12:15 EST 2022. Contains 350472 sequences. (Running on oeis4.)