OFFSET
1,1
COMMENTS
Theorem: If q=2^p-1 is a Mersenne prime greater than 3 then n=5*2^(p-1) is in the sequence.
Proof: phi(phi(n))+sigma(sigma(n))
= phi(phi(5*2^(p-1)))+sigma(sigma(5*2^(p-1)))
= phi(4*2^(p-2))+sigma(6*(2^p-1))
= 2^(p-1)+12*2^p
= 25*(2^(p-1))
= 5*n.
Note that multiplicative property of both functions phi and sigma is utilized along with the assumption p>2.
Perhaps 65792 is the only term of the sequence which is not of this form.
a(8) > 10^9. - Hiroaki Yamanouchi, Sep 19 2014
MATHEMATICA
Select[Range[2000000], EulerPhi[EulerPhi[#]]+DivisorSigma[1, DivisorSigma[1, #]]==5#&]
PROG
(PARI) isok(n) = eulerphi(eulerphi(n))+sigma(sigma(n)) == 5*n; \\ Michel Marcus, Sep 17 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jahangeer Kholdi and Farideh Firoozbakht, Sep 16 2014
STATUS
approved