Problems & Puzzles:
sigma(x) = 1 (mod x)
Farideh Firoozbakht sent the following
It is obvious that all primes
are solutions for the following equation.
sigma(x) = 1 (mod x) (*)
Q. Can you
find a composite solution for (*) ?
Antoine Verroken wrote:
According to R. Guy and G. Cohen numbers with sigma(x) = 2 * x +
1 have been called quasiperfect numbers ( they are abondant numbers
sigma(x) > 2*x ). If there exists it must be an odd square number >
10^35 and have at least 7 distinct prime factors. It is relatively
easy to prove that there exists no “ composite x “ for x = p * q and
x = p * q * r ( p,q,r primes ) with sigma = k * x + 1.