A373689 Perfect powers such that the three numbers before it and the three numbers after it are squarefree.
4, 32, 36, 216, 256, 400, 900, 1156, 1296, 1764, 2704, 2916, 3136, 3600, 4356, 5184, 6084, 7056, 8100, 8464, 9216, 11236, 12996, 16384, 19044, 20164, 20736, 22500, 25600, 26244, 26896, 31684, 32400, 36864, 38416, 39204, 40000, 41616, 44100, 46656, 49284, 51984, 54756, 55696, 57600
Offset: 1
Keywords
Examples
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 ). 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). 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).
Programs
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Mathematica
Select[Range[60000], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-3, -2, -1, 1, 2, 3}) &] (* Amiram Eldar, Jun 13 2024 *)
Comments