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 A360772 #12 Jan 05 2025 19:51:42
%S A360772 1,2,4,5,8,9,13,16,25,32,34,64,81,89,125,128,169,233,256,441,512,610,
%T A360772 625,729,1024,1156,1597,2048,2197,3025,3125,4096,4181,6561,7921,8192,
%U A360772 10946,15625,16384,20736,28561,28657,32768,39304,54289,59049,65536,75025,78125
%N A360772 List of distinct numbers that are powers of odd-indexed Fibonacci numbers or even powers of nonzero even-indexed Fibonacci numbers.
%C A360772 Ohtsuka's (2023) problem does not include 1, and includes the even powers of 8 twice (once as powers of Fibonacci(6) = 8 and once as powers of Fibonacci(3) = 2). The sum of reciprocals in this case is (61 - 15*sqrt(5))/18.
%H A360772 Amiram Eldar, <a href="/A360772/b360772.txt">Table of n, a(n) for n = 1..1000</a>
%H A360772 Hideyuki Ohtsuka, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/FQElemProbFeb2023.pdf">Problem B-1321</a>, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 61, No. 1 (2023), p. 84.
%F A360772 Sum_{n>=1} 1/a(n) = 551/126 - 5*sqrt(5)/6.
%t A360772 seq[max_] := Module[{s = {1}, k = 3, f, d}, While[(f = Fibonacci[k]) <= max, If[k != 6, d = 2 - Mod[k, 2]; s = Join[s, f^Range[d, Floor[Log[f, max]], d]]]; k++]; Sort[s]]; seq[10^5]
%Y A360772 Cf. A000045, A001519, A001906, A103323, A105317, A235383, A254719.
%K A360772 nonn
%O A360772 1,2
%A A360772 _Amiram Eldar_, Feb 20 2023