A245529 Numbers n such that 12^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.

2693, 123653, 1812389, 2349407, 12686723, 201183431, 332997529, 3822485189, 6326953051, 54520709801, 224107337017, 272603549005, 541786979683, 1035893486219, 1568751359119, 4258039403323, 5179467431095, 10293952613977, 29806275823261

Offset: 1

Author

Felix Fröhlich, Jul 25 2014

Keywords

• nonn
• more

Comments

a(8) > 10^9.

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

a(20) > 10^14. - Giovanni Resta, Jan 27 2020

Links

• Takashi Agoh, Karl Dilcher and Ladislav Skula, Fermat Quotients for Composite Moduli, J. Number Theory, Volume 66, Issue 1 (1997), 29-50.

Crossrefs

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

Programs

Maple

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

Mathematica

Select[Range[10^5], PowerMod[12, EulerPhi[#], #^2] == 1 &] (* Alonso del Arte, Jul 27 2014 *)

PARI

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

Extensions

a(8)-a(12) from Giovanni Resta, Jan 24 2020

a(13)-a(19) from Giovanni Resta, Jan 27 2020