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 A340640 #9 Jan 14 2021 15:03:06
%S A340640 4,9,25,27,32,36,49,64,81,100,121,125,128,144,196,225,243,256,289,324,
%T A340640 361,484,529,576,676,784,961,1000,1024,1089,1225,1296,1331,1369,1681,
%U A340640 1764,2025,2116,2187,2197,2209,2304,2500,2704,2809,3025,3136,3364,3481,3969
%N A340640 Perfect powers such that the two immediately adjacent perfect powers have at least one largest exponent A025479 greater than 2.
%e A340640 a(1) = 4 because the next perfect power is 8 = 2^3, i.e., its exponent is > 2.
%e A340640 a(2) = 9: the exponents of the neighbors 8 = 2^3 and 16 = 2^4 are both > 2.
%e A340640 16 is not in the sequence because both neighboring perfect powers 9 = 3^2 and 25 = 5^2 have exponents 2.
%e A340640 Neighbors with exponents > 2 of the next terms: a(3) = 25 (16 = 2^3), a(4) = 27 (32 = 2^5), a(5) = 32 (27 = 3^3), a(6) = 36 (32 = 2^5), a(7) = 49 (64 = 2^6), a(8) = 64 (81 = 3^4).
%o A340640 (PARI) a340640(limit)={my(p2=999, p1=2, n2=1, n1=4); for(n=5, limit, my(p0=ispower(n)); if(p0>1, if(p2+p0>4, print1(n1, ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
%o A340640 a340640(5000)
%Y A340640 Cf. A000290, A001597, A025479, A111245, A153158, A340586, A340641.
%K A340640 nonn
%O A340640 1,1
%A A340640 _Hugo Pfoertner_, Jan 14 2021