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A272062
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Positive numbers k such that k^2 - 1 divides 8^k - 1.
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2
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2, 4, 8, 10, 16, 22, 36, 40, 64, 96, 100, 196, 210, 256, 280, 316, 456, 560, 820, 1200, 1236, 1296, 1360, 1408, 1600, 1870, 2380, 2556, 3516, 3616, 4096, 4200, 4356, 5656, 6112, 6256, 6480, 8008, 8688, 10192, 10356, 11440, 11952, 12160, 13728, 14950, 16192, 17020, 19432, 21880, 22036
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OFFSET
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1,1
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COMMENTS
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From Robert Israel, Jun 08 2018: (Start)
All terms are even.
Are 2, 8 and 560 the only terms == 2 (mod 6)? There are no others up to 3*10^9. (End)
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..2559
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EXAMPLE
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a(1) = 2 because (8^2 - 1)/(2^2 - 1) = 21.
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MAPLE
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A272062:=n->`if`((8^n-1) mod (n^2-1) = 0, n, NULL): seq(A272062(n), n=2..5*10^4); # Wesley Ivan Hurt, Apr 21 2016
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MATHEMATICA
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Select[Range[2, 22100], Divisible[8^# - 1, #^2 - 1] &] (* Michael De Vlieger, Apr 19 2016 *)
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PROG
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(MAGMA) [0] cat [n: n in [2..30000] | Denominator((8^n-1)/(n^2-1)) eq 1];
(PARI) is(n)=Mod(8, n^2-1)^n==1 \\ Charles R Greathouse IV, Apr 19 2016
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CROSSREFS
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Cf. positive numbers n such that n^2 - 1 divides (2^k)^n - 1: A247219 (k=1), A271842 (k=2), this sequence (k=3).
Sequence in context: A025612 A102248 A161374 * A045795 A226816 A291165
Adjacent sequences: A272059 A272060 A272061 * A272063 A272064 A272065
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov, Apr 19 2016
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STATUS
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approved
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