

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, RamarĂ©, & 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

Giovanni Resta, Table of n, a(n) for n = 2..10000
F. Bertault, O. RamarĂ©, and P. Zimmermann, On sums of seven cubes, Mathematics of Computation 68 (1999), pp. 13031310.
JeanCharles Meyrignac, Computing minimal equal sums of like powers
Manfred Scheucher, Sage Script
Eric W. Weisstein, Diophantine Equation 3rd Powers
Eric W. Weisstein, Waring's Problem


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

Cf. A161882, A161884, A161885.
Sequence in context: A202258 A021540 A100199 * A248618 A197329 A046266
Adjacent sequences: A161880 A161881 A161882 * A161884 A161885 A161886


KEYWORD

nonn


AUTHOR

Dmitry Kamenetsky, Jun 21 2009


EXTENSIONS

More terms from M. F. Hasler, Dec 17 2014


STATUS

approved



