A161883 Smallest k such that n^3 = a_1^3+...+a_k^3 and all a_i are positive integers less than n.

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

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

Giovanni Resta, Table of n, a(n) for n = 2..10000

F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Mathematics of Computation 68 (1999), pp. 1303-1310.

Jean-Charles 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

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]]];
a /@ Range[2, 200] (* Jean-François Alcover, Oct 03 2020 *)

Prog

(PARI) A161883(n, verbose=0, m=3)={N=n^m; for(k=3, 99, forvec(v=vector(k-1, i, [1, n\sqrtn(k+1-i, m)]), ispower(N-sum(i=1, k-1, 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: A367409 A021540 A100199 * A248618 A197329 A360167

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