A181402 - OEIS

%I #31 May 22 2024 02:24:55

%S 1,10,73,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,

%T 121,121,121,121,121,121,121,121,121,121,121,121,121,121,121,121

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

%C An unpublished result of Deshouillers-Hennecart-Landreau, combined with Lemma 3 from Bertault, Ramaré, & Zimmermann implies that a(4)-a(34) are all 121.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

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

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

%F Conjectured g.f.: x*(1+9*x+63*x^2+48*x^3)/(1-x). - _Colin Barker_, May 04 2012

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

%Y Cf. A018890.

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

%K nonn,more

%O 1,2

%A _Martin Renner_, Jan 28 2011

%E a(5)-a(7) from _Lars Blomberg_, May 04 2011

%E a(8)-a(34) from _Charles R Greathouse IV_, Jan 23 2014