A212286 Least k > 0 such that nk = x^3 + y^3 for nonnegative coprime x and y.

1, 3, 7, 7, 21, 4, 19, 1, 37, 31, 39, 5, 2, 57, 67, 73, 7, 7, 103, 6, 133, 133, 147, 157, 18, 7, 1, 211, 237, 7, 259, 273, 301, 1, 13, 10, 4, 9, 403, 421, 3, 8, 487, 19, 541, 553, 579, 11, 637, 651, 9, 703, 31, 757, 26, 9, 853, 871, 903, 13, 27, 2, 1027, 1, 1101, 11, 1159, 1191

Offset

2,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 2..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) <= 2n^2 + 6, a(a(n)) <= n.

Example

4 is not the sum of two nonnegative cubes. 8 = 0^3 + 2^3, but 0 and 2 are not coprime. The least multiple of 4 that can be so represented is 28 = 1^3 + 3^3, so a(4) = 28/4.

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
sumOfTwoRPCubes(n)=if(sumOfTwoCubes(n), if(vecmax(factor(n)[, 2])<3, 1, for(x=ceil((n\2)^(1/3)), (n+.5)^(1/3), if(gcd(n, x)==1&&ispower(n-x^3, 3), return(1))); 0), 0)
a(n)=forstep(k=n, 2*n*(n^2+3), n, if(sumOfTwoRPCubes(k), return(k/n)))

Crossrefs

Cf. A004999, A212285, A202679.

Sequence in context: A263337 A160994 A113833 * A157102 A226512 A270307

Adjacent sequences: A212283 A212284 A212285 * A212287 A212288 A212289

Keyword

nonn

Author

Charles R Greathouse IV, Jun 12 2012

Status

approved