Perfect Totient Numbers

January 8, 2019

A perfect number is a number for which the sum of its proper divisors is equal to the number; for instance, 28 is a perfect number because it is the sum of its proper divisors 1 + 2 + 4 + 7 + 14 = 28.

A perfect totient number (A082897) is a number for which the sum of its iterated totients is equal to the number. For instance, 327 is a perfect totient number; its iterated totients are φ(327) = 216, φ(216) = 80, …, and the sum of 216 + 80 + … = 327. I love number theory; it’s totally useless, and endlessly fascinating, as you will see if you follow the links on OEIS.

Your task is to compute the perfect totient numbers less than 10,000. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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