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
Keywords
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
Programs
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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.
Comments