Problems & Puzzles: Puzzles

Puzzle 672 sigma(sigma(x)) + sigma(x) = 3x Farideh Firoozbakht sent the followig puzzle: If (3^(m+1)-1)/2 is prime then x=3^m is a solution for the following equation sigma(sigma(x)) + sigma(x) = 3x   (*) Because, sigma(x) = (3^(m+1) - 1)/2 & sigma(sigma(x)) = sigma(3^(m+1) - 1)/2 = (3^(m+1) - 1)/2 + 1 = (3^(m+1) + 1)/2, hence sigma(sigma(x)) + sigma(x) =  (3^(m+1) + 1)/2 + (3^(m+1) - 1)/2 =3^(m+1) = 3x.  Q. Does (*) has other solutions (Please see Comment lines of the sequence A090747.) ?

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