%I #20 Apr 10 2021 02:48:21

%S 1729,251,219,157,158,131,132,72,73,74,75,76,77,78,79,80,81,82,83,84,

%T 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,

%U 106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126

%N a(n) is the smallest number that is the sum of n positive cubes in two ways.

%C This is r(n,3,2) in Alter's notation.

%H R. Alter, <a href="https://doi.org/10.1007/BFb0096461">Computations and generalizations on a remark of Ramanujan</a>, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 2, page 190.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n+63 for n >= 9.

%e a(2) = 1729 = 12^3 + 1^3 = 10^3 + 9^3 (the famous Hardy-Ramanujan number).

%e a(3) = 251 = 5^3 + 5^3 + 1^3 = 6^3 + 3^3 + 2^3.

%Y Cf. A001235, A011541, A230563, A342903, A343077, A343078, A343079, A343081, A343085.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Apr 03 2021