Geodesic
On perfect totient numbers
Journal of integer sequences, Tome 6 (2003) no. 4
Let $n>2$ be a positive integer and let $\phi$ denote Euler's totient function. Define $\phi^1(n)=\phi(n)$ and $\phi^k(n)=\phi(\phi^{k-1}(n))$ for all integers $k\ge2$. Define the arithmetic function $S$ by $S(n)=\phi(n)+\phi^2(n)+\cdots+\phi^c(n)+1$, where $\phi^c(n)=2$. We say $n$ is a perfect totient number if $S(n)=n$. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence of further perfect totient numbers.
Keywords: totient, perfect totient number, class number, Diophantine equation 
@article{JIS_2003__6_4_a0,
     author = {Iannucci,  Douglas E. and Deng,  Moujie and Cohen,  Graeme L.},
     title = {On perfect totient numbers},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {4},
     zbl = {1069.11001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a0/}
}
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Iannucci,  Douglas E.; Deng,  Moujie; Cohen,  Graeme L. On perfect totient numbers. Journal of integer sequences, Tome 6 (2003) no. 4. http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a0/