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A244449 Numbers n such that phi(phi(n))+sigma(sigma(n))=5n. 2
20, 80, 320, 20480, 65792, 327680, 1310720 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=1..7.

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

Cf. A000010, A000203, A000668, A246630.

Sequence in context: A195322 A200424 A211463 * A041776 A103532 A041778

Adjacent sequences:  A244446 A244447 A244448 * A244450 A244451 A244452

KEYWORD

nonn,more

AUTHOR

Jahangeer Kholdi and Farideh Firoozbakht, Sep 16 2014

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)