Cody Problem 656 introduced the Euler totient function 
, which counts the number of integers smaller than x
, which counts the number of integers smaller than x that are relatively prime to x--that is, that share no common factors with x other than 1. Its definition implies that 
. Cody Problem 61052 deals with the Dedekind psi function 
, which is always greater than x.
. Cody Problem 61052 deals with the Dedekind psi function , which is always greater than x. What happens if the function 
is applied repeatedly? If 
, then 
and 
. The next iteration gives 
and 
. The third iteration gives 
and 
. After this step—i.e., after three iterations, the results will repeat.
is applied repeatedly? If , then and . The next iteration gives and . The third iteration gives and . After this step—i.e., after three iterations, the results will repeat. Write a function to determine the number of iterations after which repeats. In other words, determine the step at which 
.
repeats. In other words, determine the step at which . Solution Stats
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David, I get 4187, 1152, 768, 512, 256, 128, 64, 32, 16, 8, 4, 2--or 12 for 4187.
@David, I'm getting 4817, 1440, 1152, 768, 512, 256, 128, 64, 32, 16, 8, 4, 2 (length 13) for n=4817.
You are correct. I thought I had verified separately before commenting.