OFFSET
1,1
COMMENTS
This sequence consists of all primes p (for which the given ratio equals (p-1)/1, see A000040) and of composites listed in A055940 (see examples).
Up to 10^7, there is no element of this sequence having more than 2 prime factors. - M. F. Hasler, Dec 11 2007
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Douglas E. Iannucci, On the Equation sigma(n) = n + phi(n), Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.2.
FORMULA
EXAMPLE
The prime p=47 is in this sequence since phi[p]/(sigma[p]-p) = p-1 is an integer, as is the case for any other prime.
The composite n=403=13*31 is in this sequence, since the ratio phi(n)/(sigma[n]-n) =360/(1+13+31)=8 is an integer.
The first few composites in this sequence are 133,403,583,713,... (A055940).
MATHEMATICA
Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n); If[IntegerQ[s], Print[n]], {n, 2, 1000}]
Select[Range[2, 300], IntegerQ[EulerPhi[#]/(DivisorSigma[1, #]-#)]&] (* Harvey P. Dale, Dec 25 2019 *)
PROG
(PARI) for(n=2, 999, eulerphi(n)%(sigma(n)-n) || print1(n", ")) \\ M. F. Hasler, Dec 11 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 26 2002
EXTENSIONS
Edited by M. F. Hasler, Dec 11 2007
STATUS
approved