A335396 Numbers m such that sigma(m)/esigma(m) > sigma(k)/esigma(k) for all k < m, where sigma(m) is the sum of divisors of m (A000203) and esigma(m) is the sum of exponential divisors of m (A051377).
1, 2, 6, 30, 96, 210, 480, 1920, 3360, 13440, 36960, 147840, 480480, 1921920, 8168160, 11975040, 32672640, 155675520, 620780160, 1401079680, 2490808320, 2646483840
Offset: 1
Examples
The ratio sigma(m)/esigma(m) for m = 1, 2, ..., 6 is 1, 3/2, 4/3, 7/6, 6/5, 2. The record values occur at m = 1, 2 and 6.
Programs
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Mathematica
f[n_] := DivisorSigma[1,n]/( Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]); seq = {}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[seq, n]], {n, 1, 10^4}]; seq