This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A011254 #46 Sep 08 2019 17:27:41 %S A011254 23760,59400,153720,4563000,45326160,113315400,402831360,731601000, %T A011254 803685120,865950624,919501200,1178491680,3504597120,3786686400, %U A011254 6429564000,14924714400,25310621952,26998616736,53138687040,86955675840,513969369984,1054373308800,1868445408960 %N A011254 Numbers k such that phi(k) + sigma(k) = 4*k. %C A011254 If (sigma(m)-phi(m))/(4*m-sigma(m)-phi(m)) is a prime integer p not dividing m, then p*m is in the sequence. 135230346701100 is in the sequence and not divisible by 24. - _Jens Kruse Andersen_, Feb 17 2009 %C A011254 If k=80*m is in the sequence and gcd(m,10) = 1 then 200*m is also in the sequence. Proof: phi(200*m) + sigma(200*m) = phi(200)*phi(m) + sigma(200)*sigma(m) = 80*phi(m) + 465*sigma(k) = (5/2)*(32*phi(m) + 186*sigma(m)) = (5/2)*(phi(80)*phi(m) + sigma(80)*sigma(m)) = (5/2)*(phi(80*m) + sigma(80*m)) = (5/2)*(phi(k) + sigma(k)) = (5/2)*(4*k) = 5/2*(4*80*m) = 4*(200*m) so 200*m is in the sequence. - _Farideh Firoozbakht_, Mar 30 2009 %D A011254 David Wells, Prime Numbers: The Most Mysterious Figures in Math, Hoboken, New Jersey, John Wiley & Sons (2005), p. 75. %D A011254 Zhang Ming-Zhi (typescript submitted to Unsolved Problems section of Monthly, Oct 01 1996. %H A011254 Donovan Johnson, <a href="/A011254/b011254.txt">Table of n, a(n) for n = 1..25</a> (terms < 5*10^12) %H A011254 Richard K. Guy, <a href="http://www.jstor.org/stable/2974586">Divisors and desires</a>, Amer. Math. Monthly, 104 (1997), 359-360. %H A011254 Kelley Harris, <a href="http://dx.doi.org/10.1016/j.jnt.2009.02.003">On the classification of integers n that divide phi(n)+sigma(n)</a>, J. Num. Theory 129 (2009) 2093-2110 %e A011254 phi(23760) + sigma(23760) = 5760 + 89280 = 4*23760, so 23760 is in the sequence. %t A011254 Select[Range[1000000], DivisorSigma[1, #] + EulerPhi[#] == 4 # &] (* _David Nacin_, Feb 28 2012 *) %o A011254 (PARI) is(n)=eulerphi(n)+sigma(n)==4*n \\ _Charles R Greathouse IV_, Nov 27 2013 %Y A011254 Cf. A000010, A000203, A011251, A011774, A015704. %K A011254 nonn,nice %O A011254 1,1 %A A011254 _N. J. A. Sloane_ %E A011254 More terms from _Jud McCranie_ %E A011254 1178491680 from _Farideh Firoozbakht_, Jan 31 2006 %E A011254 2 more terms from _Jud McCranie_, Jan 31 2006 %E A011254 24 divides all known terms of the sequence. If this is true for the next five terms then they are 6429564000, 14924714400, 25310621952, 26998616736 and 53138687040. - _Farideh Firoozbakht_, Mar 11 2006 %E A011254 More terms from _Jens Kruse Andersen_, Feb 17 2009 %E A011254 a(21) from _Donovan Johnson_, Feb 28 2012 %E A011254 a(22)-a(23) from _Donovan Johnson_, Apr 04 2012