cp's OEIS Frontend

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

%I A336253 #19 May 06 2025 09:33:10
%S A336253 1,4,72,100,144,3528,12100,15876,24336,441000,1334025,2205000,5664400,
%T A336253 24206400,71267364,151880976,3252372552,9346201200,13319078472,
%U A336253 26828235000,347372082000,1851803856100,2260121356900,3198696480100,5202286387272,10330374528100,16316106062400
%N A336253 Exponential barely deficient numbers: exponential deficient numbers whose exponential abundancy is closer to 2 than that of any smaller exponential deficient number.
%C A336253 The exponential abundancy of a number k is esigma(k)/k, where esigma is the sum of exponential divisors of k (A051377).
%C A336253 Exponential deficient numbers are numbers k with esigma(k)/k < 2. These are numbers that are neither e-perfect (A054979) nor exponential abundant (A129575).
%C A336253 The corresponding values of the exponential abundancy are 1, 1.5, 1.666..., 1.8..., 1.833..., ...
%C A336253 All the terms are powerful numbers (A001694) because esigma(k)/k depends only on the powerful part of k (A057521). - _Amiram Eldar_, May 06 2025
%H A336253 Amiram Eldar, <a href="/A336253/b336253.txt">Table of n, a(n) for n = 1..36</a>
%e A336253 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.
%t A336253 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
%Y A336253 Cf. A051377, A054979, A057521, A129575.
%Y A336253 Subsequence of A001694.
%Y A336253 Similar sequences: A302572, A228450, A262228, A307122, A336252, A336254.
%K A336253 nonn
%O A336253 1,2
%A A336253 _Amiram Eldar_, Jul 14 2020
%E A336253 a(21)-a(27) from _Amiram Eldar_, May 06 2025