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

1,1

Comments

All terms are multiples of 4.

Links

Table of n, a(n) for n=1..44.

Example

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).

Mathematica

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

Crossrefs

Cf. A001597 (or A075090), A005117.

Subsequence of A372783.

Sequence in context: A290809 A068088 A118901 * A373689 A275713 A114076

Adjacent sequences: A373284 A373285 A373286 * A373288 A373289 A373290

Keyword

nonn

Author

Massimo Kofler, May 31 2024

Status

approved