OFFSET
1,2
COMMENTS
sigma(a(69))/(phi(a(69)) + tau(a(69))) = 857304000/23950081 ~= 35.7955.
Number of terms =< 10^k, k=0,1,2,3: 1, 5, 13, 19, 25, 29, 35, 41, 46, 50, 56, 63, 69, ..., .
All terms so far except 10, 18, 42, 84, 90 are in A025487. - David A. Corneth, Feb 14 2019
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..70
EXAMPLE
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)).
MAPLE
Res:= NULL: mx:= 0: count:= 0:
for n from 1 while count < 60 do
v:= numtheory:-sigma(n)/(numtheory:-phi(n)+numtheory:-tau(n));
if v > mx then
mx:= v;
count:= count+1;
Res:= Res, n;
fi
od:
Res; # Robert Israel, Feb 13 2019
MATHEMATICA
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Feb 13 2019
STATUS
approved