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A136540 Numbers n such that sigma(n) = 7*phi(n).

%I A136540 #25 Dec 04 2019 21:01:04
%S A136540 12,78,140,910,2214,4180,4674,8008,16120,25758,27170,46816,54530,
%T A136540 58302,94240,99484,116116,200260,233740,257140,264160,350740,371898,
%U A136540 383656,479864,518022,523218,551540,561340,575598,616722,646646,785118,965960,1027000
%N A136540 Numbers n such that sigma(n) = 7*phi(n).
%C A136540 If 2^p-1 is a Mersenne prime greater than 3 then m = 65*2^(p-2)*(2^p-1) is in the sequence (the proof is easy).
%H A136540 Amiram Eldar, <a href="/A136540/b136540.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
%H A136540 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 A136540 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 A136540 sigma(12) = 28 = 7*phi(12) so 12 is in the sequence.
%p A136540 with(numtheory): A136540:=n->`if`(sigma(n)=7*phi(n), n, NULL): seq(A136540(n), n=1..10^5); # _Wesley Ivan Hurt_, Feb 11 2017
%t A136540 Do[If[DivisorSigma[1,n]==7*EulerPhi[n],Print[n]],{n,600000}]
%t A136540 (* Second program *)
%t A136540 Select[Range[10^6], DivisorSigma[1, #] == 7 EulerPhi@ # &] (* _Michael De Vlieger_, Feb 12 2017 *)
%o A136540 (PARI) is(n)=sigma(n)==7*eulerphi(n) \\ _Charles R Greathouse IV_, May 09 2013
%Y A136540 Cf. A000043, A000668, A068390, A104900, A104901, A104902, A104903.
%K A136540 easy,nonn
%O A136540 1,1
%A A136540 _Farideh Firoozbakht_, Jan 05 2008