The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A018784 Numbers n such that sigma(phi(n)) = n. 13
 1, 3, 15, 28, 255, 744, 2418, 20440, 65535, 548856, 2835756, 4059264, 4451832, 10890040, 13192608, 23001132, 54949482, 110771178, 220174080, 445701354, 4294967295, 16331433888, 18377794080, 94951936080, 204721968000, 386940247200, 601662398400, 1433565580920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The numbers 2^2^n-1 for n=0,1,...,5 are in the sequence because 2^2^n-1=(2^2^0+1)*(2^2^1+1)*(2^2^2+1)*...*(2^2^(n-1)+1); 2^2^k+1 for k=0,1,2,3 & 4 are primes (Fermat primes); sigma(2^k)=2^(k+1)-1 and phi is a multiplicative function. Hence if p is a known Fermat prime (p=2^2^n+1 for n=0,1,2,3 & 4) then p-2 is in the sequence, note that this is not true for unknown Fermat primes if they exist. - Farideh Firoozbakht, Aug 27 2004 LINKS Graeme L. Cohen, On a conjecture of Makowski and Schinzel, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8. See Notes p. 7. FORMULA sigma(A001229), sorted. MATHEMATICA Select[Range[10^6], DivisorSigma[1, EulerPhi[#]] == # &] (* Amiram Eldar, Dec 10 2020 *) PROG (PARI) is(n)=sigma(eulerphi(n))==n \\ Charles R Greathouse IV, Nov 27 2013 CROSSREFS Cf. A097645, A097646, A019434. Sequence in context: A015646 A242571 A067144 * A147344 A201434 A308385 Adjacent sequences:  A018781 A018782 A018783 * A018785 A018786 A018787 KEYWORD nonn AUTHOR EXTENSIONS Wilson's search was complete only through a(19) = 50319360. Jud McCranie reports Jun 15 1998 that the terms through a(24) are certain. a(26)-a(28) added. Verified sequence is complete through a(28) by Donovan Johnson, Jun 30 2012 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 September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)