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

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, 211, 225, 7, 2, 273, 289, 1, 2, 10, 4, 9, 7, 421, 3, 8, 62, 19, 529, 553, 9, 7, 5, 651, 9, 703, 1, 757, 4, 9, 841, 871, 114, 13, 27, 2, 1, 1, 1089, 11, 146, 1191, 4, 1261

Offset: 1

Author

Charles R Greathouse IV, Jun 12 2012

Keywords

• nonn

Comments

Broughan calls this theta(n) and proves that it exists for all n.

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• Kevin A. Broughan, Characterizing the Sum of Two Cubes, J. Integer Seqs., Vol. 6, 2003.
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A004999, A212286.

Programs

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
a(n)=forstep(k=n,2*n*(n^2+3),n,if(sumOfTwoCubes(k),return(k/n)))

Formula

a(n) <= A212286(n) <= 2n^2 + 6, a(a(n)) <= n.