The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #11 Jul 04 2024 16:41:59
%S 4,32,36,216,256,400,900,1156,1296,1764,2704,2916,3136,3600,4356,5184,
%T 6084,7056,8100,8464,9216,11236,12996,16384,19044,20164,20736,22500,
%U 25600,26244,26896,31684,32400,36864,38416,39204,40000,41616,44100,46656,49284,51984,54756,55696,57600
%N Perfect powers such that the three numbers before it and the three numbers after it are squarefree.
%C All terms of this sequence are divisible by 4.
%e 4 = 2^2 (between 1, 2 which is a prime number, 3 which is a prime number and 5 which is a prime number, 6 = 2 * 3 and 7 which is a prime number ).
%e 32 = 2^5 (between 29 which is a prime number, 30 = 2 * 3 * 5, 31 which is a prime number and 33 = 3 * 11, 34 = 2 * 17 and 35 = 5 * 7).
%e 36 = 2^2 * 3^2 (between 33 = 3 * 11, 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19 and 39 = 3 * 13).
%t Select[Range[60000], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-3, -2, -1, 1, 2, 3}) &] (* _Amiram Eldar_, Jun 13 2024 *)
%Y Intersection of A001597 (or A075090) and A068088.
%Y Cf. A005117, A373077, A373287.
%K nonn
%O 1,1
%A _Massimo Kofler_, Jun 13 2024