A104902 - OEIS

%I #21 Dec 04 2019 18:19:17

%S 210,1848,2970,3720,6270,26796,38340,53940,59340,60960,70686,78210,

%T 80940,88536,129540,142290,149226,155064,174174,237000,249210,300390,

%U 350610,385710,429408,526110,604128,624840,664608,827310,828072,842010,848040,906528

%N Numbers n such that sigma(n) = 12*phi(n).

%C If p>2 and 2^p-1 is prime (a Mersenne prime) then 15*2^(p-2)*(2^p-1) is in the sequence. So 15*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence.

%H Amiram Eldar, <a href="/A104902/b104902.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)

%H Kevin A. Broughan and Daniel Delbourgo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Broughan/broughan26.html">On the Ratio of the Sum of Divisors and Euler’s Totient Function I</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.

%H Kevin A. Broughan and Qizhi Zhou, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Broughan/bro32.html">On the Ratio of the Sum of Divisors and Euler's Totient Function II</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.

%e p>2, q=2^p-1(q is prime); m=15*2^(p-2)*q so sigma(m)=24*(2^(p-1)-1)*2^p=12*(8*2^(p-3)*(2^p-2))=12*phi(m) hence m is in the sequence.

%e sigma(237000)=748800=12*62400=12*phi(237000) so 237000 is in the sequence but 237000 is not of the form 15*2^(p-2)*(2^p-1).

%t Do[If[DivisorSigma[1, m] == 12*EulerPhi[m], Print[m]], {m, 1200000}]

%o (PARI) is(n)=sigma(n)==12*eulerphi(n) \\ _Charles R Greathouse IV_, May 09 2013

%Y Cf. A000043, A062699, A068390, A104900, A104901.

%K easy,nonn

%O 1,1

%A _Farideh Firoozbakht_, Apr 01 2005