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%I #36 Apr 03 2021 00:32:42
%S 5,27,251,2673,1375298099,160426514
%N Smallest number that is the sum of three positive n-th powers in at least two ways.
%C a(7) > 10^26 (if it exists). - _Donovan Johnson_, Nov 22 2013
%C a(7) > 33055^7 ~ 4.31*10^31 (if it exists). _Duncan Moore_, Oct 07 2017
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, section 21.11.
%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. The value for a(6) given in Table 5 is wrong.
%e 5 = 1^1 + 1^1 + 3^1 = 1^1 + 2^1 + 2^1.
%e 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2.
%e 251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3.
%e 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4.
%e 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5.
%e 160426514 = 3^6 + 19^6 + 22^6 = 10^6 + 15^6 + 23^6.
%Y Cf. A046093, A230477, A230561, A230562.
%K hard,more,nice,nonn
%O 1,1
%A _Jonathan Sondow_, Oct 25 2013
%E a(4) and a(5) corrected by _Donovan Johnson_, Oct 28 2013
%E Edited by _N. J. A. Sloane_, Apr 03 2021
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