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%I #11 Sep 20 2019 21:08:40
%S 1,2,3,4,5,6,8,10,12,14,18,21,22,24,30,40,42,54,66,72,78,88,96,102,
%T 114,120,168,210,216,264,312,330,360,378,384,408,456,480,510,546,552,
%U 600,672,690,696,744,840,1080,1320,1512,1560,1848,1920,2040,2184,2280,2688
%N Infinitary highly abundant numbers: numbers m such that isigma(m) > isigma(k) for all k < m, where isigma(k) is the sum of infinitary divisors of n (A049417).
%C The infinitary version of A002093.
%H Amiram Eldar, <a href="/A327634/b327634.txt">Table of n, a(n) for n = 1..930</a>
%e The first 10 values of isigma(k) for k = 1 to 10 are: 1, 3, 4, 5, 6, 12, 8, 15, 10, 18. Record values are reached for all these values of k except for 7 and 9, therefore the sequence begins with 1, 2, 3, 4, 5, 6, 8, 10, ...
%t f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); isigma[1] = 1; isigma[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) + 1); seq = {};sm = 0; Do[s = isigma[n]; If[s > sm, sm = s; AppendTo[seq, n]], {n, 1, 10^4}]; seq
%Y Cf. A002093, A037992, A049417, A285614, A292983.
%K nonn,look
%O 1,2
%A _Amiram Eldar_, Sep 20 2019
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