%I #6 May 30 2020 19:13:16
%S 1,2,6,12,30,168,210,420,840,9240,83160,120120,5165160,26860680,
%T 277560360,569729160,16522145640,33044291280,563462139240,
%U 1140028049160,1255683068640,65361608151840,299761858075680,413956851628320
%N Balanced numbers (A020492) k with a record value of sigma(k)/phi(k).
%C The corresponding record values are 1, 3, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 28, 30, 31, 32, 33, 35, 36, 38, 39, ...
%C The terms were calculated using data from _Jud McCranie_.
%e The first 4 balanced numbers are k = 1, 2, 3, 6. The corresponding values of sigma(k)/phi(k) = A000203(k)/A000010(k) are 1, 3, 2, 6. The record values, 1, 3 and 6 occur at 1, 2 and 6 - the first 3 terms of this sequence.
%t s = {}; rm = 0; Do[r = DivisorSigma[1, n]/EulerPhi[n]; If[IntegerQ[r] && r > rm, rm = r; AppendTo[s, n]], {n, 1, 120120}]; s
%Y Cf. A000010, A000203, A018894, A020492.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, May 30 2020