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%I #8 Jun 13 2021 03:23:57
%S 1,4,16,144,1296,3600,20736,32400,176400,518400,1587600,12960000,
%T 25401600,635040000,3073593600
%N Numbers m such that sigma(m)/isigma(m) > sigma(k)/isigma(k) for all k < m, where sigma(m) is the sum of divisors of m (A000203) and isigma(m) is the sum of infinitary divisors of m (A049417).
%e The ratio sigma(m)/isigma(m) for m = 1, 2, 3 and 4 is 1, 1, 1 and 7/5. The record values occur at m = 1 and 4.
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, 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]; f[n_] := DivisorSigma[1,n] / isigma[n]; s={}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 2 * 10^5}]; s
%Y Cf. A000203, A049417, A285906, A335396.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jun 05 2020
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