A319314 Numbers k such that 2^phi(k) == phi(k)^2 (mod k^2).

1, 3, 4, 5, 6, 8, 10, 12, 384, 640, 768, 896, 960, 24576, 49152, 950272, 1425408, 1572864, 3145728, 10485760, 19398656, 65011712, 100663296, 110057537, 201326592, 220115074, 671088640, 1879048192

Offset: 1

Author

Altug Alkan, Sep 17 2018

Keywords

• nonn
• more

Comments

Sequence is infinite, i.e., 3*2^(3*(t-1)-(-1)^t) is a term for all t > 0.

Prime terms (5, 110057537, ...) are in A246568 based on case A = +1.

Crossrefs

Cf. A077815, A077816, A246568, A292544.

Programs

Magma

[1] cat [n: n in [1..10^6] | 2^EulerPhi(n) mod n^2 eq EulerPhi(n)^2]; // Vincenzo Librandi, Sep 20 2018

PARI

isok(n) = Mod(2, n^2)^eulerphi(n)==eulerphi(n)^2;