A248862 -id:A248862 - cp's OEIS frontend

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

Farideh Firoozbakht, Dec 12 2014

nonn

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

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

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

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

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

cp's OEIS Frontend

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

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