A373287 Perfect powers such that the two numbers before and the two numbers after are squarefree.

4, 32, 36, 144, 216, 256, 400, 900, 1156, 1296, 1728, 1764, 2704, 2916, 3136, 3600, 4356, 5184, 6084, 7056, 8100, 8464, 9216, 11236, 12100, 12996, 16384, 19044, 20164, 20736, 22500, 25600, 26244, 26896, 31684, 32400, 36864, 38416, 39204, 40000, 41616, 44100, 45796, 46656

Offset: 1

Author

Massimo Kofler, May 31 2024

Keywords

• nonn

Comments

All terms are multiples of 4.

Examples

			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).
32 = 2^5 (between 30 = 2 * 3 * 5, 31 which is a prime number and 33 = 3 * 11, 34 = 2 * 17).
36 = 2^2 * 3^2 (between 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19).
		

Crossrefs

Cf. A001597 (or A075090), A005117.

Subsequence of A372783.

Programs

Mathematica

Select[Range[50000], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-2, -1, 1, 2}) &] (* Amiram Eldar, May 31 2024 *)