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 A246630 Numbers n such that phi(phi(n)) + sigma(sigma(n))=6*n. 2
 344, 4016, 16064, 39208, 69430, 130250, 1028096, 1210928, 4843712, 16449536, 65798144, 309997568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Theorem: If q=2^p-1 is a Mersenne prime greater than 7 then n=251*2^(p-1) is in the sequence. Proof:  phi(phi(n))+sigma(sigma(n))       = phi(phi(251*2^(p-1)))+sigma(sigma(251*2^(p-1)))       = phi(125*2^(p-1))+sigma(252*(2^p-1))       = 100*2^(p-2)+sigma(2^2*3^2*7)*2^p       = 25*2^p+7*13*8*2^p       = 753*2^p       = 6*n. Note that multiplicative property of both functions phi and sigma is utilized along with the assumption p>3. The first four terms of the sequence of the above form are 4016, 16064, 1028096 and 16449536. If q = 2^p-1 is a Mersenne prime greater than 7 then n = 75683*2^(p-1) is in the sequence. - Hiroaki Yamanouchi, Sep 19 2014 a(13) > 2*10^9. - Hiroaki Yamanouchi, Sep 19 2014 251 and 75683 are both primes satisfying phi(phi(p)) + 4*sigma(sigma(p)) = 12*p. - Michel Marcus, Sep 20 2014 LINKS MATHEMATICA Do[If[EulerPhi[EulerPhi[n]]+DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 16500000}] PROG (PARI) for(n=1, 10^9, if(sigma(sigma(n))+eulerphi(eulerphi(n)) == 6*n, print1(n, ", "))) \\ Derek Orr, Sep 19 2014 CROSSREFS Cf. A000010, A000203, A000668, A244449. Sequence in context: A183680 A183674 A245994 * A250921 A262791 A186935 Adjacent sequences:  A246627 A246628 A246629 * A246631 A246632 A246633 KEYWORD nonn,more AUTHOR Jahangeer Kholdi and Farideh Firoozbakht, Sep 16 2014 EXTENSIONS a(11)-a(12) from Hiroaki Yamanouchi, Sep 19 2014 STATUS approved

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Last modified May 23 21:03 EDT 2022. Contains 353993 sequences. (Running on oeis4.)