OFFSET
1,2
COMMENTS
Up to 1.5*10^8 there exist 43 terms of the sequence. - Farideh Firoozbakht, Apr 15 2006
If p=3*2^n-1 is an odd prime then m=2^n*p is in the sequence. Proof: sigma(m)-m=(2^(n+1)-1)*(p+1)-2^n*p=2*(2^(n-1)*(p-1))= 2*phi(m), so sigma(m)=m mod(phi(m)). Hence for n>0, 2^A002235(n)* (3*2^A002235(n)-1) is in the sequence and 2^164987*(3*2^164987-1) is the largest known term of the sequence. - Farideh Firoozbakht, Apr 15 2006
LINKS
Jud McCranie, Table of n, a(n) for n = 1..100 (First 71 terms from Donovan Johnson, a(72)-a(93) from Giovanni Resta).
Douglas E. Iannucci, On the Equation sigma(n) = n + phi(n), Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.2.
EXAMPLE
sigma(10) = 18 is congruent to 10 mod phi(10) = 4, so 10 is a term of the sequence.
MATHEMATICA
Select[ Range[ 1, 10^5 ], Mod[ DivisorSigma[ 1, # ], EulerPhi[ # ] ] == Mod[ #, EulerPhi[ # ] ] & ]
PROG
(PARI) is(n)=sigma(n)==Mod(n, eulerphi(n)) \\ Charles R Greathouse IV, Feb 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 11 2002
EXTENSIONS
More terms from Jason Earls, Jan 14 2002
More terms from Farideh Firoozbakht, Apr 15 2006
STATUS
approved