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A336253
Exponential barely deficient numbers: exponential deficient numbers whose exponential abundancy is closer to 2 than that of any smaller exponential deficient number.
2
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..., ...
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
Similar sequences: A302572, A228450, A262228, A307122, A336252, A336254.
Sequence in context: A161791 A132097 A128062 * A227248 A113839 A077112
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 14 2020
STATUS
approved