This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016078 #32 Feb 16 2025 08:32:33
%S A016078 4,50,1729,635318657
%N A016078 Smallest number that is sum of 2 positive n-th powers in 2 different ways.
%C A016078 If it exists, a(5) > 1.02*10^26 (see eqn. (27) at the Mathworld link). - _Jon E. Schoenfield_, Jan 05 2019
%H A016078 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.
%H A016078 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation5thPowers.html">Diophantine Equation--5th Powers</a>
%F A016078 If A230561(n) exists, then a(n) <= A230561(n) for n > 1, with equality at least for n = 2, and inequality at least for n = 3. - _Jonathan Sondow_, Oct 24 2013 [Comment edited by _N. J. A. Sloane_, Apr 03 2021]
%e A016078 4 = 1^1 + 3^1 = 2^1 + 2^1;
%e A016078 50 = 1^2 + 7^2 = 5^2 + 5^2,
%e A016078 1729 = 1^3 + 12^3 = 9^3 + 10^3;
%e A016078 635318657 = 59^4 + 158^4 = 133^4 + 134^4 = A018786(1).
%t A016078 (* This is just an empirical verification *) Do[max = 4 + n^4; Clear[cnt]; cnt[_] = 0; smallest = Infinity; Do[ cnt[an = x^n + y^n] += 1; If[cnt[an] == 2 && an < smallest, smallest = an], {x, 1, max}, {y, x, max}]; Print["a(", n, ") = ", smallest], {n, 1, 4}] (* _Jean-François Alcover_, Aug 13 2013 *)
%Y A016078 Cf. A046881, A230561.
%K A016078 nonn,nice,hard,more
%O A016078 1,1
%A A016078 _Robert G. Wilson v_, Dec 11 1999