A014946 Numbers k that divide 6^k-1.

1, 5, 25, 125, 625, 1555, 3125, 7775, 15625, 38875, 78125, 194375, 390625, 483605, 971875, 1953125, 2418025, 4859375, 9673655, 9765625, 12090125, 24296875, 48368275, 48828125, 60450625, 120909025, 121484375, 150401155, 241841375

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Comments

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.

From Alexander Adamchuk, May 16 2010: (Start)

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

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

Crossrefs

Cf. A024062 (6^n-1).

Programs

Mathematica

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

PARI

is(n)=Mod(6,n)^n==1 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

Better description from Benoit Cloitre, Mar 06 2002

Edited and extended by Robert G. Wilson v, Jun 18 2002

a(25)-a(45) from Alexander Adamchuk, May 16 2010