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 A291851 #10 Apr 05 2021 20:43:08
%S A291851 4,128,972,1089,4096,12500,31104,34848,59536,67228,75625,131072,
%T A291851 236196,264627,400000,644204,995328,1050625,1115136,1485172,1605289,
%U A291851 1905152,2151296,2420000,3037500,3403125,4194304,5679428,7558272,8468064,9771876,9904396,9966649
%N A291851 Numbers k such that k^3 is the sum of two positive 5th powers.
%C A291851 If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^2)^3 is a cube. Therefore the square of each term of A003347 is a term of this sequence.
%C A291851 When k is in this sequence, k * (n^5), for n > 1, is also in this sequence.
%e A291851 4^3 = 2^6 = 2^5 + 2^5, so 4 is in the sequence.
%e A291851 1089^3 = 33^5 + 66^5, so 1089 is in the sequence.
%t A291851 lst={};Do[If[IntegerQ[(n^3-a^5)^(1/5)],AppendTo[lst,n]],{n,10^7},{a,(n^3/2)^(1/5)}]; lst
%Y A291851 Cf. A000404, A004431, A003325, A050801, A003336, A003347.
%K A291851 nonn
%O A291851 1,1
%A A291851 _XU Pingya_, Sep 04 2017