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 A104901 Numbers n such that sigma(n) = 8*phi(n). 11
 42, 594, 744, 1254, 7668, 8680, 10788, 11868, 12192, 14630, 15642, 16188, 25908, 28458, 49842, 60078, 70122, 77142, 105222, 124968, 125860, 138460, 142240, 165462, 168402, 169608, 188860, 201924, 242316, 259160, 302260, 553000, 561906, 700910, 726440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p>3 and 2^p-1 is prime (a Mersenne prime) then 35*2^(p-2)*(2^p-1) is in the sequence. So 35*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence. If p>2 and 2^p-1 is prime (a Mersenne prime) then 3*2^(p-2)*(2^p-1) is in the sequence (the proof is easy). - Farideh Firoozbakht, Dec 23 2007 LINKS Donovan Johnson, Table of n, a(n) for n = 1..1000 Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Eulerâ€™s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8. Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2. EXAMPLE p>3, q=2^p-1(q is prime); m=35*2^(p-2)*q so sigma(m)=48*(2^(p-1)-1)*2^p=8*(24*2^(p-3)*(2^p-2))=8*phi(m) hence m is in the sequence. sigma(553000) = 1497600 = 8*187200 = 8*phi(553000) so 553000 is in the sequence but 553000 is not of the form 35*2^(p-2)*(2^p-1). MATHEMATICA Do[If[DivisorSigma[1, m] == 8*EulerPhi[m], Print[m]], {m, 1000000}] Select[Range[800000], DivisorSigma[1, #]==8*EulerPhi[#]&] (* Harvey P. Dale, Sep 12 2018 *) PROG (PARI) is(n)=sigma(n)==8*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013 CROSSREFS Cf. A000043, A062699, A068390, A104900, A104902. Sequence in context: A245874 A293096 A279888 * A091962 A269659 A007746 Adjacent sequences:  A104898 A104899 A104900 * A104902 A104903 A104904 KEYWORD easy,nonn AUTHOR Farideh Firoozbakht, Apr 01 2005 STATUS approved

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Last modified January 17 16:11 EST 2019. Contains 319235 sequences. (Running on oeis4.)