A018890 Numbers whose smallest expression as a sum of positive cubes requires exactly 7 cubes.

7, 14, 21, 42, 47, 49, 61, 77, 85, 87, 103, 106, 111, 112, 113, 122, 140, 148, 159, 166, 174, 178, 185, 204, 211, 223, 229, 230, 237, 276, 292, 295, 300, 302, 311, 327, 329, 337, 340, 356, 363, 390, 393, 401, 412, 419, 427, 438, 446, 453, 465, 491, 510, 518, 553, 616

Offset: 1

Author

Anonymous

Keywords

• nonn
• fini

Comments

It is conjectured that a(121)=8042 is the last term - Jud McCranie

An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that if there are any terms beyond a(121) = 8042,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

References

• J. Roberts, Lure of the Integers, entry 239.

Links

• T. D. Noe, Table of n, a(n) for n = 1..121
• F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Math. Comp. 68 (1999), pp. 1303-1310.
• Jan Bohman and Carl-Erik Froberg, Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
• K. S. McCurley, An effective seven-cube theorem, J. Number Theory, 19 (1984), 176-183.
• Eric Weisstein's World of Mathematics, Cubic Number
• Eric Weisstein's World of Mathematics, Waring's Problem
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A004829, A018888, A018889.

Programs

Mathematica

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