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 A350430 #23 Jan 27 2022 20:57:41 %S A350430 1,625,157464 %N A350430 a(n) is the smallest n-th power which can be represented as the sum of n distinct positive n-th powers in exactly n ways, or -1 if none exists. %C A350430 From _Jon E. Schoenfield_, Dec 30 2021: (Start) %C A350430 222000^4 < a(4) < 4891341^4 = lcm(2829, 12259, 16359, 30381)^4 (see A039664, including the Wroblewski link). %C A350430 10000^5 <= a(5) < 12528^5 = lcm(72, 1044, 1392, 2088, 3132)^5 (see A063923, including the Waldby link; note that, although the terms of A063923 include 72, 144, 1044, 1392, and 2088, whose LCM is only 4176, the primitive solution in which the sum of 5 distinct 5th powers is 144^5 is 0^5 + 27^5 + 84^5 + 110^5 + 133^5 = 144^5, which is not the sum of 5 positive n-th powers). %C A350430 Conjecture: a(6) = -1. (End) %e A350430 For n = 2: 625 = 25^2 = 7^2 + 24^2 = 15^2 + 20^2. %e A350430 For n = 3: 157464 = 54^3 = 6^3 + 36^3 + 48^3 = 12^3 + 19^3 + 53^3 = 27^3 + 36^3 + 45^3. %Y A350430 Cf. A007666, A025303, A025401, A030052, A039664, A063923, A146756, A230718, A331675. %K A350430 nonn,bref,hard,more %O A350430 1,2 %A A350430 _Ilya Gutkovskiy_, Dec 30 2021