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%I A332039 #11 Feb 06 2020 00:48:06
%S A332039 1,12,24,60,120,240,360,720,1440,2880,4320,5760,7200,8640,11520,14400,
%T A332039 17280,21600,25920,28800,34560,43200,60480,86400,120960,129600,172800,
%U A332039 241920,259200,302400,345600,483840,518400,604800,907200,1036800,1209600,1814400,2419200
%N A332039 Indices of records in A332038.
%C A332039 Numbers k such that isigma(x) = k has more solutions x than any smaller k, where isigma(x) is the sum of infinitary divisors of x (A049417).
%C A332039 The infinitary version of A145899.
%C A332039 The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).
%H A332039 Amiram Eldar, <a href="/A332039/b332039.txt">Table of n, a(n) for n = 1..53</a>
%H A332039 Amiram Eldar, <a href="/A332039/a332039.txt">Table of n, a(n), A332038(a(n)) for n = 1..53</a>
%e A332039 There are 3 solutions to isigma(x) = 24: isigma(14) = isigma(15) = isigma(23) = 24. For all m < 24 there are 2 or fewer solutions to isigma(x) = m, thus 24 is in the sequence.
%t A332039 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]); m = 10000; v = Table[0, {m}]; Do[i = isigma[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
%Y A332039 Cf. A145899, A049417, A289132, A332037, A332038, A332041.
%K A332039 nonn
%O A332039 1,2
%A A332039 _Amiram Eldar_, Feb 05 2020

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