%I #20 Jan 27 2020 15:44:02

%S 2693,123653,1812389,2349407,12686723,201183431,332997529,3822485189,

%T 6326953051,54520709801,224107337017,272603549005,541786979683,

%U 1035893486219,1568751359119,4258039403323,5179467431095,10293952613977,29806275823261

%N Numbers n such that 12^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.

%C a(8) > 10^9.

%C If a(n) is prime, it is in A111027.

%C a(20) > 10^14. - _Giovanni Resta_, Jan 27 2020

%H Takashi Agoh, Karl Dilcher and Ladislav Skula, <a href="http://dx.doi.org/10.1006/jnth.1997.2162">Fermat Quotients for Composite Moduli</a>, J. Number Theory, Volume 66, Issue 1 (1997), 29-50.

%p with(numtheory): A245529:=n->`if`( (12 &^ phi(n)-1) mod n^2 = 0, n, NULL): seq(A245529(n), n=2..10^4); # _Wesley Ivan Hurt_, Jul 26 2014

%t Select[Range[10^5], PowerMod[12, EulerPhi[#], #^2] == 1 &] (* _Alonso del Arte_, Jul 27 2014 *)

%o (PARI) for(n=2, 1e9, if(Mod(12, n^2)^(eulerphi(n))==1, print1(n, ", ")))

%Y Cf. A000010, A077816, A242958, A242959, A242960, A111027.

%K nonn,more

%O 1,1

%A _Felix Fröhlich_, Jul 25 2014

%E a(8)-a(12) from _Giovanni Resta_, Jan 24 2020

%E a(13)-a(19) from _Giovanni Resta_, Jan 27 2020