A004825 Numbers that are the sum of at most 3 positive cubes.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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.
• Index entries for sequences related to sums of cubes

Crossrefs

A003072 is a subsequence.

Cf. A004999.

Column k=3 of A336820.

Programs

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 *)

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