%I #13 May 26 2024 03:57:15

%S 1,2,4,8,10,16,20,32,40,50,64,68,80,100,110,128,136,160,164,200,220,

%T 250,256,272,320,328,340,400,440,500,512,544,550,610,640,656,680,772,

%U 800,820,880,1000,1010,1024,1088,1100,1156,1210,1220,1250,1280,1312,1360

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

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

%C 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.

%H Amiram Eldar, <a href="/A093547/b093547.txt">Table of n, a(n) for n = 1..10000</a>

%t v={};Do[If[IntegerQ[(3^n^2-1)/n], v=Append[v, n];Print[v]], {n, 2500}]

%t Select[Range[1400],Divisible[3^#^2-1,#]&] (* _Harvey P. Dale_, Nov 04 2015 *)

%o (PARI) isok(k) = Mod(3, k)^(k^2) == 1; \\ _Amiram Eldar_, May 26 2024

%Y Cf. A067945, A093546, A006521.

%K nonn

%O 1,2

%A _Farideh Firoozbakht_, Mar 31 2004