On perfect totient numbers

• Main Author: Belmonte, Jovele G.
• Format: text
• Language: English
• Published: Animo Repository 2006
• Subjects: Perfect numbers; Number theory; Euler's numbers; Arithmetic functions; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/3449; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/10287/viewcontent/CDTG004177_P__1_.pdf
• Institution: De La Salle University

This thesis is an exposition of the paper On Perfect Totient Numbers by Douglas E. Iannuci, Deng Moujie and Graeme L. Cohen which appeared in the Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.5. Let n > 2 be a positive integer and let denote Eulers totient function. Define 1(n) = (n) and k(n) = ( k1(n)) for all integers k 2. Define the arithmetic function S by S(n) = (n) + 2(n) + . . . + c(n) + 1, where 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 and non-existence of further perfect totient numbers. An original contribution of this study are additional forms of perfect totient numbers.