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A373287
Perfect powers such that the two numbers before and the two numbers after are squarefree.
1
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.
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
Subsequence of A372783.
Sequence in context: A290809 A068088 A118901 * A373689 A275713 A114076
KEYWORD
nonn
AUTHOR
Massimo Kofler, May 31 2024
STATUS
approved