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A248861
Numbers k such that phi(k)^phi(k) == 1 (mod sigma(k)).
2
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.
Subsequence of A055008. - Jason Yuen, Jul 01 2024
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
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Dec 12 2014
STATUS
approved