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%I #34 Jun 11 2024 09:52:47
%S 4,32,36,144,216,256,400,900,1156,1296,1728,1764,2704,2916,3136,3600,
%T 4356,5184,6084,7056,8100,8464,9216,11236,12100,12996,16384,19044,
%U 20164,20736,22500,25600,26244,26896,31684,32400,36864,38416,39204,40000,41616,44100,45796,46656
%N Perfect powers such that the two numbers before and the two numbers after are squarefree.
%C All terms are multiples of 4.
%e 4 = 2^2 (between 2 which is a prime number, 3 which is a prime number and 5 which is a prime number, 6 = 2 * 3).
%e 32 = 2^5 (between 30 = 2 * 3 * 5, 31 which is a prime number and 33 = 3 * 11, 34 = 2 * 17).
%e 36 = 2^2 * 3^2 (between 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19).
%t Select[Range[50000], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-2, -1, 1, 2}) &] (* _Amiram Eldar_, May 31 2024 *)
%Y Cf. A001597 (or A075090), A005117.
%Y Subsequence of A372783.
%K nonn
%O 1,1
%A _Massimo Kofler_, May 31 2024
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