%I #35 Aug 10 2022 09:50:37

%S 7,14,21,42,47,49,61,77,85,87,103,106,111,112,113,122,140,148,159,166,

%T 174,178,185,204,211,223,229,230,237,276,292,295,300,302,311,327,329,

%U 337,340,356,363,390,393,401,412,419,427,438,446,453,465,491,510,518,553,616

%N Numbers whose smallest expression as a sum of positive cubes requires exactly 7 cubes.

%C It is conjectured that a(121)=8042 is the last term - _Jud McCranie_

%C An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that if there are any terms beyond a(121) = 8042, they are greater than 1.62 * 10^34. - _Charles R Greathouse IV_, Jan 23 2014

%D J. Roberts, Lure of the Integers, entry 239.

%H T. D. Noe, <a href="/A018890/b018890.txt">Table of n, a(n) for n = 1..121</a>

%H F. Bertault, O. Ramaré, and P. Zimmermann, <a href="https://doi.org/10.1090/S0025-5718-99-01071-6">On sums of seven cubes</a>, Math. Comp. 68 (1999), pp. 1303-1310.

%H Jan Bohman and Carl-Erik Froberg, <a href="http://dx.doi.org/10.1007/BF01934077">Numerical investigation of Waring's problem for cubes</a>, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.

%H K. S. McCurley, <a href="http://dx.doi.org/10.1016/0022-314X(84)90100-8">An effective seven-cube theorem</a>, J. Number Theory, 19 (1984), 176-183.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%t Select[Range[700], (pr = PowersRepresentations[#, 7, 3]; pr != {} && Count[pr, r_/; (Times @@ r) == 0] == 0)&] (* _Jean-François Alcover_, Jul 26 2011 *)

%Y Cf. A004829, A018888, A018889.

%K nonn,fini

%O 1,1

%A Anonymous