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 A104903 Numbers n such that sigma(n) = 16*phi(n). 6
 20790, 26040, 43890, 268380, 368280, 377580, 415380, 426720, 547470, 566580, 777480, 906780, 996030, 1659000, 1744470, 2102730, 2179320, 2454270, 2699970, 3682770, 4373880, 5053860, 5340060, 5791170, 5874660, 5894070, 5936280, 6035040, 7067340, 8013060 (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 105*2^(p-2)*(2^p-1) is in the sequence. So 105*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence. It seems that 10 divides all terms of this sequence. 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>2, q=2^p-1(q is prime); m=105*2^(p-2)*q so sigma(m)=192*(2^(p-1)-1)*2^p=16*(48*2^(p-3)*(2^p-2))=16*phi(m) hence m is in the sequence. sigma(1659000)=5990400=16*374400=16*phi(1659000) so 1659000 is in the sequence but 1659000 is not of the form 105*2^(p-2)*(2^p-1). MATHEMATICA Do[If[DivisorSigma[1, m] == 16*EulerPhi[m], Print[m]], {m, 10000000}] PROG (PARI) is(n)=sigma(n)==16*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013 CROSSREFS Cf. A000043, A062699, A068390, A104900, A104901, A104902. Sequence in context: A173572 A048960 A252331 * A235952 A207794 A256840 Adjacent sequences:  A104900 A104901 A104902 * A104904 A104905 A104906 KEYWORD easy,nonn AUTHOR Farideh Firoozbakht, Apr 01 2005 STATUS approved

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Last modified October 15 04:45 EDT 2018. Contains 316200 sequences. (Running on oeis4.)