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A004825
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Numbers that are the sum of at most 3 positive cubes.
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17
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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
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listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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MAPLE
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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:
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:
# 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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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