A336253 Exponential barely deficient numbers: exponential deficient numbers whose exponential abundancy is closer to 2 than that of any smaller exponential deficient number.

1, 4, 72, 100, 144, 3528, 12100, 15876, 24336, 441000, 1334025, 2205000, 5664400, 24206400, 71267364, 151880976, 3252372552, 9346201200, 13319078472, 26828235000

Offset

1,2

Comments

The exponential abundancy of a number k is esigma(k)/k, where esigma is the sum of exponential divisors of k (A051377).

Exponential deficient numbers are numbers k with esigma(k)/k < 2. These are numbers that are neither e-perfect (A054979) nor exponential abundant (A129575).

The corresponding values of the exponential abundancy are 1, 1.5, 1.666..., 1.8..., 1.833..., ...

Links

Table of n, a(n) for n=1..20.

Example

4 is a term since it is exponential deficient, and esigma(4)/4 = 3/2 is higher than esigma(k)/k for all the exponential deficient numbers k < 4.

Mathematica

fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ fun @@@ FactorInteger[n]; rm = 0; s={}; Do[r = esigma[n]/n; If[r >= 2, Continue[]]; If[r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^6}]; s

Crossrefs

Cf. A051377, A054979, A129575.

Similar sequences: A302572, A228450, A262228, A307122, A336252, A336254.

Sequence in context: A161791 A132097 A128062 * A227248 A113839 A077112

Adjacent sequences: A336250 A336251 A336252 * A336254 A336255 A336256

Keyword

nonn,more

Author

Amiram Eldar, Jul 14 2020

Status

approved