

A018784


Numbers n such that sigma(phi(n)) = n.


14



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
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OFFSET

1,2


COMMENTS

The numbers 2^2^n1 for n=0,1,...,5 are in the sequence because 2^2^n1=(2^2^0+1)*(2^2^1+1)*(2^2^2+1)*...*(2^2^(n1)+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 p2 is in the sequence, note that this is not true for unknown Fermat primes if they exist.  Farideh Firoozbakht, Aug 27 2004


LINKS



FORMULA



MATHEMATICA

Select[Range[10^6], DivisorSigma[1, EulerPhi[#]] == # &] (* Amiram Eldar, Dec 10 2020 *)


PROG



CROSSREFS



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



