A093547 Numbers k such that k divides 3^(k^2) - 1.

1, 2, 4, 8, 10, 16, 20, 32, 40, 50, 64, 68, 80, 100, 110, 128, 136, 160, 164, 200, 220, 250, 256, 272, 320, 328, 340, 400, 440, 500, 512, 544, 550, 610, 640, 656, 680, 772, 800, 820, 880, 1000, 1010, 1024, 1088, 1100, 1156, 1210, 1220, 1250, 1280, 1312, 1360

Offset: 1

Author

Farideh Firoozbakht, Mar 31 2004

Keywords

• nonn

Comments

This sequence is closed under multiplication, i.e., if x and y are terms then so is x*y.

A067945 is a subsequence of this sequence. A067945 is also closed under multiplication. In fact if m is an integer and k is a natural number then the sequence " n divides m^(n^k) - 1 " is a subsequence of the sequence " n divides m^n^(k+1)- 1 " and both are closed under multiplication.

Links

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

Crossrefs

Cf. A067945, A093546, A006521.

Programs

Mathematica

v={};Do[If[IntegerQ[(3^n^2-1)/n], v=Append[v, n];Print[v]], {n, 2500}]
Select[Range[1400],Divisible[3^#^2-1,#]&] (* Harvey P. Dale, Nov 04 2015 *)

PARI

isok(k) = Mod(3, k)^(k^2) == 1; \\ Amiram Eldar, May 26 2024