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%I #29 Dec 10 2020 17:28:15
%S 1,3,15,28,255,744,2418,20440,65535,548856,2835756,4059264,4451832,
%T 10890040,13192608,23001132,54949482,110771178,220174080,445701354,
%U 4294967295,16331433888,18377794080,94951936080,204721968000,386940247200,601662398400,1433565580920
%N Numbers n such that sigma(phi(n)) = n.
%C 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
%H Graeme L. Cohen, <a href="http://matwbn.icm.edu.pl/ksiazki/cm/cm74/cm7411.pdf">On a conjecture of Makowski and Schinzel</a>, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8. See Notes p. 7.
%F sigma(A001229), sorted.
%t Select[Range[10^6], DivisorSigma[1, EulerPhi[#]] == # &] (* _Amiram Eldar_, Dec 10 2020 *)
%o (PARI) is(n)=sigma(eulerphi(n))==n \\ _Charles R Greathouse IV_, Nov 27 2013
%Y Cf. A097645, A097646, A019434.
%K nonn
%O 1,2
%A _David W. Wilson_
%E Wilson's search was complete only through a(19) = 50319360. _Jud McCranie_ reports Jun 15 1998 that the terms through a(24) are certain.
%E a(26)-a(28) added. Verified sequence is complete through a(28) by _Donovan Johnson_, Jun 30 2012
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