Problems & Puzzles: Puzzles

Puzzle 435. φ(x) + σ(x) = k.x Farideh Firoozbakht poses the following question: Maybe some of your puzzlers can find next term (or more terms) of the sequence A015704.  A015704: 1, 312, 23760, x x=smallest m such that φ(m) + σ(m)=5m. We know all solutions of the equation phi(x)+sigma(x)=2*x (1 & all primes). Also we know some solutions of the equations φ(x) + σ(x) = k.x ; k=3 & 4 (please see A011774 & A011254).  But we don't know even one solution for the equations phi(x)+sigma(x)=k*x  where k>4 and I'd like to know some of them.

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Juan López sent the following contribution (March 08)

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