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%I #4 May 21 2020 21:20:16
%S 945,29835,33345,43065,46035,49875,83265,354585,359205,361515,366135,
%T 382305,389235,400785,403095,407715,414645,416955,423885,430815,
%U 437745,442365,77967015,132335385,210124665,719709375,724239285,1756753845,9665740455,10394173335
%N Odd infinitary abundant numbers whose infinitary abundancy is closer to 2 than that of any smaller odd 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).
%e The infinitary abundancies of the first terms are 2.031..., 2.027..., 2.015..., 2.006..., 2.001..., ...
%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, 10^5, 2}]; seq
%Y Cf. A049417, A127666, A188263, A335052, A335053, A335054.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 21 2020
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