A181402 Total number of positive integers below 10^n requiring 7 positive cubes in their representation as sum of cubes.

1, 10, 73, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121

Offset: 1

Author

Martin Renner, Jan 28 2011

Keywords

• nonn
• more

Comments

An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that a(4)-a(34) are all 121. Probably a(n) = 121 for all n > 3. - Charles R Greathouse IV, Jan 23 2014

Links

• F. Bertault, O. Ramaré, and P. Zimmermann, On sums of seven cubes, Math. Comp. 68 (1999), pp. 1303-1310.
• Eric Weisstein's World of Mathematics, Waring's Problem.

Crossrefs

Cf. A018890.

Cf. A002283, A061439, A130130, A181375, A181377, A181379, A181381, A181400, A181404.

Formula

A061439(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + a(n) + A181404(n) + A130130(n) = A002283(n).

Conjectured g.f.: x*(1+9*x+63*x^2+48*x^3)/(1-x). - Colin Barker, May 04 2012

Conjectured e.g.f.: 121*(exp(x) - 1) - 120*x - 111*x^2/2 - 8*x^3. - Stefano Spezia, May 21 2024

Extensions

a(5)-a(7) from Lars Blomberg, May 04 2011

a(8)-a(34) from Charles R Greathouse IV, Jan 23 2014