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A373689
Perfect powers such that the three numbers before it and the three numbers after it are squarefree.
0
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
1,1
COMMENTS
All terms of this sequence are divisible by 4.
EXAMPLE
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).
MATHEMATICA
Select[Range[60000], GCD @@ FactorInteger[#][[;; , 2]] > 1 && And @@ SquareFreeQ /@ (# + {-3, -2, -1, 1, 2, 3}) &] (* Amiram Eldar, Jun 13 2024 *)
CROSSREFS
Intersection of A001597 (or A075090) and A068088.
Sequence in context: A068088 A118901 A373287 * A275713 A114076 A078092
KEYWORD
nonn
AUTHOR
Massimo Kofler, Jun 13 2024
STATUS
approved