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A212286 Least k > 0 such that nk = x^3 + y^3 for nonnegative coprime x and y. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)