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Numbers k that divide 6^k-1.
16

%I #21 Jun 28 2021 04:06:05

%S 1,5,25,125,625,1555,3125,7775,15625,38875,78125,194375,390625,483605,

%T 971875,1953125,2418025,4859375,9673655,9765625,12090125,24296875,

%U 48368275,48828125,60450625,120909025,121484375,150401155,241841375

%N Numbers k that divide 6^k-1.

%C Includes all powers of 5. If a term such as 1555 = 5*311 occurs, so does any number of the form 5^a * 311^b for a>3.

%C From _Alexander Adamchuk_, May 16 2010: (Start)

%C All terms that are not powers of 5 are divisible by 5 and 311.

%C Prime divisors of a(n) are {5, 311, 6221, 15551, 155501, ...}. (End)

%t Select[ Range[ 5*10^7], PowerMod[6, #, # ] == 1 & ]

%o (PARI) is(n)=Mod(6,n)^n==1 \\ _Charles R Greathouse IV_, Nov 04 2016

%Y Cf. A024062 (6^n-1).

%K nonn

%O 1,2

%A _Olivier GĂ©rard_

%E Better description from _Benoit Cloitre_, Mar 06 2002

%E Edited and extended by _Robert G. Wilson v_, Jun 18 2002

%E a(25)-a(45) from _Alexander Adamchuk_, May 16 2010