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

1,3

Comments

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

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

Formula

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

Example

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.

Prog

(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)))

Crossrefs

Cf. A004999, A212286.

Sequence in context: A106167 A194473 A091913 * A192789 A026136 A026172

Adjacent sequences: A212282 A212283 A212284 * A212286 A212287 A212288

Keyword

nonn

Author

Charles R Greathouse IV, Jun 12 2012

Status

approved