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 A373867 #27 Jun 22 2024 22:08:43 %S A373867 8,32,100,512,33554432,36893488147419103232, %T A373867 2923003274661805836407369665432566039311865085952, %U A373867 78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831281613255980613632 %N A373867 Perfect powers of the form x^y + y^x, where x > 1 and y > 1. %C A373867 Subsequence of A076980: a(n) is a Leyland number that is a perfect power. The condition that x > 1 and y > 1 is necessary, otherwise every perfect power would belong to this sequence, since m^n = (m^n-1)^1 + 1^(m^n-1). %C A373867 If x = y = 2^k, then x^y + y^x = 2^(k*2^k + 1) belongs to this sequence for all k > 0, and (k*2^k + 1) is the k-th Cullen number. That is, 2^A002064(k) is a term, with k > 0, from which it follows that this sequence has infinitely many terms. %C A373867 Conjecture: 32 and 100 are the only terms for which x != y: 2^4 + 4^2 = 2^5 = 32 and 2^6 + 6^2 = 10^2 = 100. %e A373867 100 is a term, because 100 = 10^2 and 100 = 2^6 + 6^2. %Y A373867 Cf. A001597, A002064, A076980. %K A373867 nonn %O A373867 1,1 %A A373867 _Gonzalo MartÃnez_, Jun 21 2024