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A212285 Least k > 0 such that nk = x^3 + y^3 for nonnegative x and y.

%I A212285 #12 May 13 2013 01:54:21
%S A212285 1,1,3,2,7,9,4,1,1,25,31,6,5,2,57,1,73,3,7,14,6,121,133,3,5,18,1,1,
%T A212285 211,225,7,2,273,289,1,2,10,4,9,7,421,3,8,62,19,529,553,9,7,5,651,9,
%U A212285 703,1,757,4,9,841,871,114,13,27,2,1,1,1089,11,146,1191,4,1261
%N A212285 Least k > 0 such that nk = x^3 + y^3 for nonnegative x and y.
%C A212285 Broughan calls this theta(n) and proves that it exists for all n.
%H A212285 Charles R Greathouse IV, <a href="/A212285/b212285.txt">Table of n, a(n) for n = 1..1000</a>
%H A212285 Kevin A. Broughan, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.html">Characterizing the Sum of Two Cubes</a>, J. Integer Seqs., Vol. 6, 2003.
%H A212285 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A212285 a(n) <= A212286(n) <= 2n^2 + 6, a(a(n)) <= n.
%e A212285 3 is not the sum of two nonnegative cubes, nor is 6. But 9 = 2^3 + 1^3 and so a(3) = 9/3 = 3.
%o A212285 (PARI) sumOfTwoCubes(n)=my(k1=ceil((n-1/2)^(1/3)), k2=floor((4*n+1/2)^(1/3)), L); fordiv(n,d,if(d>=k1 && d<=k2 && denominator(L=(d^2-n/d)/3)==1 && issquare(d^2-4*L), return(1))); 0
%o A212285 a(n)=forstep(k=n,2*n*(n^2+3),n,if(sumOfTwoCubes(k),return(k/n)))
%Y A212285 Cf. A004999, A212286.
%K A212285 nonn
%O A212285 1,3
%A A212285 _Charles R Greathouse IV_, Jun 12 2012