%I #41 Jun 08 2022 14:48:43

%S 1,2,4,6,10,12,18,24,30,42,60,84,90,120,180,210,360,420,840,1260,1680,

%T 2520,4620,7560,9240,13860,18480,27720,55440,110880,120120,180180,

%U 240240,360360,720720,1441440,2162160,3603600,4084080,4324320,6126120,12252240,24504480

%N Numbers n such that sigma(n)/(phi(n) + tau(n)) is a record.

%C sigma(a(69))/(phi(a(69)) + tau(a(69))) = 857304000/23950081 ~= 35.7955.

%C Number of terms =< 10^k, k=0,1,2,3: 1, 5, 13, 19, 25, 29, 35, 41, 46, 50, 56, 63, 69, ..., .

%C All terms so far except 10, 18, 42, 84, 90 are in A025487. - _David A. Corneth_, Feb 14 2019

%H Robert G. Wilson v, <a href="/A324059/b324059.txt">Table of n, a(n) for n = 1..70</a>

%e a(7) = 18 since it is the first number greater than a(6) such that sigma(18)/(phi(18) + tau(18)) = 13/4 > 14/5 = sigma(12)/(phi(12) + tau(12)).

%p Res:= NULL: mx:= 0: count:= 0:

%p for n from 1 while count < 60 do

%p v:= numtheory:-sigma(n)/(numtheory:-phi(n)+numtheory:-tau(n));

%p if v > mx then

%p mx:= v;

%p count:= count+1;

%p Res:= Res, n;

%p fi

%p od:

%p Res; # _Robert Israel_, Feb 13 2019

%t k = 1; mx = 0; lst = {}; While[k < 25000000, If[ DivisorSigma[1, k] > mx (EulerPhi[k] + DivisorSigma[0, k]), mx = DivisorSigma[1, k]/(EulerPhi[k] + DivisorSigma[0, k]); AppendTo[lst, k]]; k ++]; lst

%t DeleteDuplicates[Table[{n,DivisorSigma[1,n]/(EulerPhi[n]+DivisorSigma[0,n])},{n,2451*10^4}],GreaterEqual[#1[[2]],#2[[2]]]&][[All,1]] (* _Harvey P. Dale_, Jun 08 2022 *)

%o (PARI) lista(nn) = {my(m=0, newm); for (n=1, nn, newm = sigma(n)/(eulerphi(n) + numdiv(n)); if (newm > m, print1(n, ", "); m = newm););} \\ _Michel Marcus_, Feb 13 2019

%Y Cf. A000010, A000005, A000203, A061468, A324060, A025487.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Feb 13 2019