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%I #7 Aug 20 2019 07:24:13
%S 4,9,16,25,27,32,64,81,125,128,169,243,256,441,512,625,729,1024,1156,
%T 2048,2187,2197,3025,3125,4096,6561,7921,8192,9261,15625,16384,19683,
%U 20736,28561,32768,39304,54289,59049,65536,78125,131072,142129,166375,177147
%N Perfect powers of Fibonacci numbers: a(n) = F(m)^k for appropriate m > 2 and k > 1, with F = A000045.
%C Suggested by _R. J. Mathar_'s comment in A105317.
%H Reinhard Zumkeller, <a href="/A254719/b254719.txt">Table of n, a(n) for n = 1..10000</a>
%e . A254719 | |4| |9| |16| |25|27|32| |64|81| |125|128| |169
%e . +-------+-+---+-+--+--+--+--+--+--+-----+--+--+--+---+---+---+---
%e . A105317 |0|1|2|3|4|5|8|9|13|16|21|25|27|32|34|55|64|81|89|125|128|144|169
%e . +-+-+-+-+-+-+-+-+--+--+--+--------+--+--+-----+--+-------+---+---
%e . A000045 |0|1|2|3| |5|8| |13| |21| |34|55| |89| |144|
%o (Haskell)
%o a254719 n = a254719_list !! (n-1)
%o a254719_list = g (0 : drop 2 a000045_list) a105317_list where
%o g fs'@(f:fs) (x:xs) = if x == f then g fs xs else x : g fs' xs
%Y A105317 without A000045; cf. A001597.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Feb 06 2015
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