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%I #23 Sep 08 2022 08:45:53
%S 1,3,5,15,21,39,55,57,105,111,155,165,195,205,219,273,285,327,399,465,
%T 505,555,609,615,741,777,903,915,1095,1155,1255,1265,1365,1443,1515,
%U 1533,1635,1705,1995,2067,2109,2145,2255,2265,2289,2373,2667,2715,2847
%N Numbers k such that k^3 divides 16^(k^2) - 1.
%C From _Robert Israel_, Apr 24 2015: (Start)
%C The only primes in the sequence are 3 and 5.
%C If m and n are in the sequence and are coprime, then m*n is in the sequence.
%C Are all members of the sequence divisible by 3 or 5? (End)
%H Robert Israel, <a href="/A177916/b177916.txt">Table of n, a(n) for n = 1..1000</a>
%p A177916:=n->`if`((16&^(n^2)-1) mod n^3 = 0, n, NULL): seq(A177916(n), n=1..1000); # _Wesley Ivan Hurt_, Apr 23 2015
%t Select[Range[3000], IntegerQ[(16^(#^2) - 1) / #^3 ] &] (* _Vincenzo Librandi_, Apr 24 2015 *)
%o (Magma) [n: n in [1..2000] | Denominator((16^(n^2) - 1)/n^3) eq 1]; // _Vincenzo Librandi_, Apr 24 2015
%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
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