A067947 Numbers k such that k divides 7^k - 1.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 32, 36, 40, 48, 54, 57, 60, 64, 72, 80, 81, 96, 100, 108, 114, 120, 128, 144, 156, 160, 162, 171, 180, 192, 200, 216, 220, 228, 240, 243, 256, 258, 272, 288, 300, 312, 320, 324, 333, 342, 360, 384, 400, 432, 440, 456

Offset: 1

Author

Benoit Cloitre, Mar 05 2002

Keywords

• easy
• nonn

Comments

For k >= 0, 2^k is in the sequence.

From Alexander Adamchuk, Jan 05 2007: (Start)

3^k is in the sequence.

k! is in the sequence for k < 7.

k!/7 is in the sequence for 7 <= k < 14.

k!/7^2 is in the sequence for 14 <= k < 21.

k!/7^3 is in the sequence for 21 <= k < 28.

k!/7^4 is in the sequence for k = 28. (End)

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A127107 (k^2 divides 7^k - 1).

Programs

Magma

[n: n in [1..500] | (7^n-1) mod n eq 0 ]; // Vincenzo Librandi, Apr 24 2017

Mathematica

Select[Range[600], Divisible[7^# - 1, #] &] (* Vincenzo Librandi, Apr 24 2017 *)
Join[{1},Select[Range[500],PowerMod[7,#,#]==1&]] (* Harvey P. Dale, Jan 22 2025 *)

PARI

is(n)=Mod(7,n)^n==1 \\ Charles R Greathouse IV, Nov 04 2016