A100827 - OEIS (original) (raw)

Each number k on this list has more solutions to the equation x - phi(x) = k (where phi is Euler's totient function, A000010) than any preceding k except 1.

This sequence is a subset of A063741. As noted in that sequence, there are infinitely many solutions to x - phi(x) = 1. Unlike A097942, the highly totient numbers, this sequence has many odd numbers besides 1.

With the expection of 2, 4, 8, all of the known terms are congruent to -1 mod a primorial (A002110). The specific primorial satisfying this congruence would result in a sequence similar to A080404 a(n)=A007947[A055932(n)]. - Wilfredo Lopez (chakotay147138274(AT)yahoo.com), Dec 28 2006

Because most of the solutions to x - phi(x) = k are semiprimes p*q with p+q=k+1, it appears that this sequence eventually has terms that are one less than the Goldbach-related sequence A082917. In fact, terms a(108) to a(176) are A082917(n)-1 for n=106..174. [T. D. Noe, Mar 16 2010] This holds through a(229). [Jud McCranie, May 18 2017]