

A161883


Smallest k such that n^3 = a_1^3+...+a_k^3 and all a_i are positive integers less than n.


6



8, 6, 5, 7, 3, 4, 5, 3, 5, 5, 3, 4, 4, 5, 5, 5, 3, 3, 3, 4, 5, 4, 3, 3, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 5, 3, 4, 3, 4, 4, 3, 3, 4, 3, 3, 3, 4, 3, 5, 4, 3, 4, 4, 3, 3, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3
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OFFSET

2,1


COMMENTS

It follows from Wieferich's result g(3) = 9 that a(n) <= 10. Theorem 2 of Bertault, Ramaré, & Zimmermann can be used to show that a(n) <= 8 (check congruence classes of cubes mod 333 with one summand of 1, 8, or 27). Probably a(2), a(3), and a(5) are the only members greater than 5 in this sequence.  Charles R Greathouse IV, Jul 30 2011


LINKS

F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Mathematics of Computation 68 (1999), pp. 13031310.


MATHEMATICA

f[n_, k_] := Select[PowersRepresentations[n^3, k, 3], AllTrue[#, 0<#<n&]&];
a[n_] := For[k = 3, True, k++, If[f[n, k] != {}, Print[n, " ", k]; Return[k]]];


PROG

(PARI) A161883(n, verbose=0, m=3)={N=n^m; for(k=3, 99, forvec(v=vector(k1, i, [1, n\sqrtn(k+1i, m)]), ispower(Nsum(i=1, k1, v[i]^m), m, &K)&&K>0&&!if(verbose, print1("/*"n" "v"*/"))&&return(k), 1))} \\ M. F. Hasler, Dec 17 2014


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



