A248861 Numbers k such that phi(k)^phi(k) == 1 (mod sigma(k)).

1, 2, 8, 36, 128, 225, 289, 578, 900, 2025, 2601, 3600, 10404, 32768, 41616, 45369, 57600, 242064, 665856, 725904, 783225, 1134225, 1140624, 1782225, 1988100, 2903616, 3132900, 4862025, 6155361, 6275025, 7128900, 7868025, 8625969, 10208025, 13505625

Offset: 1

Author

Farideh Firoozbakht, Dec 12 2014

Keywords

• nonn

Comments

2^m is a term of the sequence if and only if m=2^j-1 where j is a nonnegative integer. Hence the sequence is infinite.

289 is a term of the sequence which is of the form p^2 where p is prime. What is the next such term?

578 is a term of the sequence which is not of the form 2^m or m^2. What is the next such term?

A248862 gives primes p such that 900*p^2 is a term of the sequence.

Subsequence of A055008. - Jason Yuen, Jul 01 2024

Links

• Jason Yuen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A177006, A248862, A055008.

Programs

Mathematica

Prepend[Select[Range[30000], Mod[EulerPhi[#]^EulerPhi[#], DivisorSigma[1, #]] == 1 &], 1] (* Michael De Vlieger, Dec 13 2014 *)

PARI

isok(n) = my(in = eulerphi(n)); lift(Mod(in, sigma(n))^in - 1) == 0; \\ Michel Marcus, Dec 13 2014