A123091 Numbers k such that k divides 5^k - 5.

1, 2, 3, 4, 5, 7, 10, 11, 13, 15, 17, 19, 20, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 124, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 190, 191, 193, 197, 199, 211, 217, 223, 227, 229, 233, 239

Offset: 1

Author

Alexander Adamchuk, Nov 04 2006

Keywords

• nonn

Comments

All primes are the terms of a(n). Nonprimes in a(n) are listed in A122782(n) = {1,4,10,15,20,65,124,190,217,310,435,561,781,...}. All pseudoprimes to base 5 are the terms of a(n). They are listed in A005936(n) = {4,124,217,561,781,...}. Numbers n up to 10^6 such that n divides 5^n + 5 are {1,2,5,6,10,30,70,1565,2806,3126,51670,58290,214405,285286,378258}.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A122782 (nonprimes n such that 5^n==5 (mod n)).

Cf. A005936 (pseudoprimes to base 5).

Cf. A067946 (numbers n such that n divides 5^n-1).

Cf. A015951 (numbers n such that n | 5^n + 1).

Programs

Mathematica

Select[Range[1000], IntegerQ[(PowerMod[5,#,# ]-5)/# ]&]

PARI

is(n)=Mod(5,n)^n==5 \\ Charles R Greathouse IV, Nov 04 2016