OFFSET
1,1
COMMENTS
Obviously, C(p) = (p-phi(p))/(p-1) = 1/(p-1), i.e., A160598(p)=1, for all primes p. This sequence lists composite numbers for which C(n) has denominator 1, i.e., n-1 is a multiple of n - phi(n).
The sequence contains numbers F(k)*F(k+1)*...*F(k+d), if the factors are successive Fermat primes F(k)=2^(2^k)+1.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..1000
Laurentiou Panaitopol, On some Properties Concerning the Function a(n)=n-phi(n), Bull. Greek Math. Soc., p. 71-77, Vol 45, 2001.
Project Euler, Problem 245: Coresilience, May 2009.
EXAMPLE
a(1)=15 is in the sequence, because for n=15, we have (n - phi(n))/(n-1) = (15-8)/14 = 1/2; apart from the primes, this is the smallest number n such that C(n) is a unit fraction.
MATHEMATICA
Select[Range[400000], CompositeQ[#]&&Divisible[#-1, #-EulerPhi[#]]&] (* Harvey P. Dale, Apr 23 2019 *)
PROG
(PARI) for(n=2, 10^9, isprime(n) & next; (n-1)%(n-eulerphi(n)) || print1(n", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 23 2009
EXTENSIONS
Offset changed from 2 to 1 by Donovan Johnson, Jan 12 2012
STATUS
approved
