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

1,2

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.

Links

Table of n, a(n) for n=1..35.

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A000203, A177006, A248862.

Sequence in context: A236626 A355102 A355104 * A323677 A295501 A283847

Adjacent sequences: A248858 A248859 A248860 * A248862 A248863 A248864

Keyword

nonn

Author

Farideh Firoozbakht, Dec 12 2014

Status

approved