OFFSET
1,1
COMMENTS
sigma is the multiplicative sum-of-divisors function.
phi is Euler's totient.
Complete through 25558816403.
All given here are products of powers of consecutive Fermat primes based on generalized repunit primes; see links.
It is conjectured (see links) that all odd solutions are of this form, for which at least 10130 solutions are known.
REFERENCES
Richard Guy, "Unsolved Problems in Number Theory", section B42
Oystein Ore, "Number Theory and Its History", 1948, reprinted 1988, Dover, ISBN-10: 0486656209, pp. 88 et seq., 109 et seq.
LINKS
Walter Nissen, phi(sigma(n)) = sigma(phi(n))
EXAMPLE
sigma(9) = 13, phi(9) = 6, sigma(6) = phi(13) = 12, so 9 is in the sequence.
PROG
(PARI) isok(n) = (n % 2) && (eulerphi(sigma(n)) == sigma(eulerphi(n))) \\ Michel Marcus, Jul 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Nissen, Apr 26 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Oct 28 2009
STATUS
approved