This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066679 Numbers n such that sigma(n) is congruent to n mod phi(n). 2
 1, 2, 6, 10, 12, 44, 90, 184, 440, 528, 588, 672, 752, 3796, 8928, 9888, 12224, 35640, 37680, 49024, 50976, 89152, 94200, 108192, 146412, 159840, 279864, 1734720, 2554368, 2977920, 12580864, 14239872, 16544880, 28321920, 41362200, 56976480, 60610624 (list; graph; refs; listen; history; text; internal format)
 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 Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..93 (terms < 10^13, first 71 terms from Donovan Johnson) 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 Cf. A000010, A002235. Sequence in context: A277238 A108783 A235989 * A086123 A144031 A190055 Adjacent sequences:  A066676 A066677 A066678 * A066680 A066681 A066682 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 11:12 EDT 2019. Contains 324152 sequences. (Running on oeis4.)