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

1,2

Links

Table of n, a(n) for n=1..22.

Example

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.

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

Crossrefs

Cf. A000203, A051377, A285906, A335400.

Sequence in context: A088857 A099081 A051844 * A034501 A203461 A071758

Adjacent sequences: A335393 A335394 A335395 * A335397 A335398 A335399

Keyword

nonn,more

Author

Amiram Eldar, Jun 05 2020

Status

approved