On Perfect Totient Numbers
Abstract
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>=2. Define the arithmetic function S by S(n)=phi(n)+phi^2(n)+...+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.
- Publication:
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Journal of Integer Sequences
- Pub Date:
- December 2003
- Bibcode:
- 2003JIntS...6...45I
- Keywords:
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- Number Theory