Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.2

Primes in Classes of the Iterated Totient Function

Tony D. Noe
14025 NW Harvest Lane
Portland, OR 97229


As shown by Shapiro, the iterated totient function separates integers into classes having three sections. After summarizing some previous results about the iterated totient function, we prove five theorems about primes p in a class and the factorization of p-1. An application of one theorem is the calculation of the smallest number in classes up to 1000.

Full version:  pdf,    dvi,    ps,    latex     Errata, November 18 2008    

(Concerned with sequences A005239 A007755 A058811 A058812 A092878 and A136040 .)

Received December 14 2007; revised version received January 7 2008. Published in Journal of Integer Sequences, January 13 2008.

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