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A104900 Numbers n such that sigma(n) = 6*phi(n).

%I A104900 #21 Dec 04 2019 18:18:35
%S A104900 6,70,616,1240,2090,8932,17980,19780,20320,26980,29512,43180,49742,
%T A104900 51688,58058,79000,100130,116870,128570,175370,176715,201376,208280,
%U A104900 221536,275770,280670,282680,302176,373065,427924,435435,470764,483616,618772,642124
%N A104900 Numbers n such that sigma(n) = 6*phi(n).
%C A104900 If p>2 & 2^p-1 is prime (a Mersenne prime) then 5*2^(p-2)*(2^p-1) is in the sequence. So 5*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence.
%H A104900 Amiram Eldar, <a href="/A104900/b104900.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
%H A104900 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 A104900 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 A104900 p>2, q=2^p-1(q is prime); m=5*2^(p-2)*q so sigma(m)=6*(2^(p-1)-1)*2^p=6*phi(m) hence m is in the sequence.
%e A104900 sigma(79000)=187200=6*31200 =6*phi(79000) so 79000 is in the sequence but 79000 is not of the form 5*2^(p-2)*(2^p-1).
%t A104900 Do[If[DivisorSigma[1, m] == 6*EulerPhi[m], Print[m]], {m, 1000000}]
%o A104900 (PARI) is(n)=sigma(n)==6*eulerphi(n) \\ _Charles R Greathouse IV_, May 09 2013
%o A104900 (PARI) v=List(); forfactored(n=6,10^6, if(sigma(n)==6*eulerphi(n), listput(v,n[1]))); Vec(v) \\ _Charles R Greathouse IV_, May 09 2017
%Y A104900 Cf. A000043, A062699, A068390, A104901.
%K A104900 nonn
%O A104900 1,1
%A A104900 _Farideh Firoozbakht_, Apr 01 2005