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%I #26 Apr 18 2021 17:51:20
%S 5104,1225,766,221,222,223,224,197,163,164,165,166,139,140,141,142,
%T 143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,
%U 160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177
%N a(n) is the smallest number that is the sum of n positive cubes in three or more ways.
%C This is r(n,3,3) 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 7, page 192.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = n + 124 for n >= 15.
%e a(3) = 5104 = 1^3 + 12^3 + 15^3 = 2^3 + 10^3 + 16^3 = 9^3 + 10^3 + 15^3.
%e a(4) = 1225 = 1^3 + 2^3 + 6^3 + 10^3 = 3^3 + 7^3 + 7^3 + 8^3 = 4^3 + 6^3 + 6^3 + 9^3.
%e a(9) = 224 = 6^3 + 8*1^3 = 3*4^3 + 3^3 + 5*1^3 = 5^3 + 4^3 + 4*2^3 + 3*1^3.
%Y Cf. A342902, A343080, A343082, A343083, A343085.
%K nonn,easy
%O 3,1
%A _Sean A. Irvine_, Apr 04 2021
%E Corrected by _Robert Israel_, Apr 05 2021
%E a(9) reverted by _Sean A. Irvine_, Apr 18 2021