A319383 Numbers k such that phi(k)^phi(k) == 1 (mod k^2).

1, 2, 19043, 289627, 6674419, 49865347, 185014655

Offset: 1

Author

Altug Alkan, Sep 18 2018

Keywords

• nonn
• more

Comments

All terms are cyclic numbers (A003277).

The next term, if it exists, is > 10^10. - Vaclav Kotesovec, Oct 23 2018

a(8) > 10^12, if it exists. - Giovanni Resta, Oct 25 2018

Crossrefs

Cf. A000010, A003277, A063439, A077816.

Programs

Mathematica

Select[Range[20000], Divisible[EulerPhi[#]^EulerPhi[#] - 1, #^2] &] (* Vaclav Kotesovec, Oct 21 2018 *)
Join[{1},Select[Range[1851*10^5],With[{c=EulerPhi[#]},PowerMod[c,c,#^2] == 1&]]] (* Harvey P. Dale, Oct 09 2020 *)

PARI

isok(n) = Mod(eulerphi(n), n^2)^eulerphi(n)==1;
for(n=1, 10000000, if(isok(n),print1(n, ", ")))