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 A246802 Solutions of sigma(sigma(x)) - phi(phi(x)) = 5x. 0
 92, 368, 712, 1472, 94208, 1507328, 6029312, 37412864, 24696061952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Theorem: If 2^p-1 is a Mersenne prime greater than 3, then x = 23*2^(p-1) is a solution to the equation, sigma(sigma(x)) - phi(phi(x)) = 5x. Proof:  sigma(sigma(x))- phi(phi(x))       = sigma(sigma(23*2^(p-1))) - phi(phi(23*2^(p-1)))       = sigma(24*(2^p-1)) - phi(22*2^(p-2))       = 60*2^p - 10*2^(p-2)       = 115*2^(p-1)       = 5*x. The multiplicative property of both functions phi and sigma is applied along with the assumption p>2. Note that 712 and 37412864 are two terms of the sequence which are not of the form mentioned in the theorem. a(10) > 10^11. - Hiroaki Yamanouchi, Sep 11 2015 LINKS MATHEMATICA Do[If[DivisorSigma[1, DivisorSigma[1, n]]-EulerPhi[EulerPhi[n]]==5n, Print[n]], {n, 230000000}] PROG (PARI) is(n)=sigma(sigma(n)) - eulerphi(eulerphi(n)) == 5*n \\ Anders HellstrÃ¶m, Sep 11 2015 CROSSREFS Cf. A000010, A000203, A000668, A137600, A244449, A246630. Sequence in context: A044805 A063326 A185461 * A302351 A100169 A100170 Adjacent sequences:  A246799 A246800 A246801 * A246803 A246804 A246805 KEYWORD nonn,more AUTHOR Jahangeer Kholdi and Farideh Firoozbakht, Sep 17 2014 EXTENSIONS a(9) from Hiroaki Yamanouchi, Sep 11 2015 STATUS approved

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Last modified May 7 05:10 EDT 2021. Contains 343636 sequences. (Running on oeis4.)