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A212285 Least k > 0 such that nk = x^3 + y^3 for nonnegative x and y. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 18:44 EDT 2021. Contains 343987 sequences. (Running on oeis4.)