login
Numbers k such that k^3 divides 9^(k^2) - 1.
15

%I #32 Jun 06 2021 09:04:13

%S 1,2,4,8,10,20,40,68,82,110,136,164,220,328,340,410,440,610,680,772,

%T 820,1010,1210,1220,1510,1544,1640,2020,2420,2440,2530,2788,3020,3740,

%U 3860,4040,4510,4840,5060,5576,6040,6710,6806,7004,7370,7480,7720,8020,9020

%N Numbers k such that k^3 divides 9^(k^2) - 1.

%H Robert Price, <a href="/A177909/b177909.txt">Table of n, a(n) for n = 1..446</a> (terms 1..119 from R. J. Mathar).

%e 9^(2^2) - 1 = 6560, which is divisible by 2^3, so 2 is in the sequence.

%e 9^(4^2) - 1 = 1853020188851840, which is divisible by 4^3, so 4 is in the sequence.

%e 9^(6^2) - 1 = 22528399544939174411840147874772640, which is not divisible by 6, and certainly not by 6^3, so 6 is not in the sequence.

%p A177909:=n->`if`(9^(n^2)-1 mod n^3 = 0,n,NULL): seq(A177909(n), n=1..1000); # _Wesley Ivan Hurt_, Oct 04 2014

%t Select[Range[100], Divisible[9^(#^2) - 1, #^3] &] (* _Alonso del Arte_, Oct 04 2014 *)

%Y Cf. A068382 (k divides 9^k-1), A127101 (k^2 divides 9^k-1).

%Y Cf. A129211, A129212, A177905, A127106, A177907, A127102, A177909, A177243.

%Y Cf. A177911, A177912, A177913, A177914, A177915, A177916, A177917, A177918, A177919, A177920.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, May 14 2010