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%I #7 May 23 2020 05:32:36
%S 24,30,40,54,56,70,88,104,642,654,678,726,762,786,822,834,894,906,942,
%T 978,1002,1014,1038,1074,1086,1146,1158,1182,1194,1266,1338,1362,1374,
%U 1398,1434,1446,1506,1536,1542,1578,1596,2406,2454,2514,2526,2586,2598,2634
%N Infinitary barely abundant numbers: infinitary abundant numbers whose infinitary abundancy is closer to 2 than that of any smaller infinitary abundant number.
%C The infinitary abundancy of a number k is isigma(k)/k, where isigma(k) is the sum of infinitary divisors of k (A049417).
%H Amiram Eldar, <a href="/A335054/b335054.txt">Table of n, a(n) for n = 1..10000</a>
%e The infinitary abundancies of the first terms are 2.5, 2.4, 2.25, 2.222..., 2.142..., 2.057..., ...
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; seq = {}; r = 3; Do[s = isigma[n]/n; If[s > 2 && s < r, AppendTo[seq, n]; r = s], {n, 1, 3000}]; seq
%Y The infinitary version of A071927.
%Y Cf. A049417, A129656, A302570, A302571.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 21 2020
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