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Indices of records in A332036.
4

%I #10 Feb 06 2020 00:48:17

%S 1,12,24,60,120,240,360,720,1440,2160,2880,4320,5760,7200,8640,12960,

%T 14400,17280,21600,25920,28800,30240,34560,40320,43200,51840,60480,

%U 86400,120960,172800,181440,241920,259200,302400,362880,483840,518400,604800,725760,907200

%N Indices of records in A332036.

%C Numbers k such that bsigma(x) = k has more solutions x than any smaller k, where bsigma(x) is the sum of bi-unitary divisors of x (A188999).

%C The bi-unitary version of A145899.

%C The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).

%H Amiram Eldar, <a href="/A332037/b332037.txt">Table of n, a(n) for n = 1..58</a>

%H Amiram Eldar, <a href="/A332037/a332037.txt">Table of n, a(n), A332036(a(n)) for n = 1..58</a>

%e There are 3 solutions to bsigma(x) = 24: bsigma(14) = bsigma(15) = bsigma(23) = 24. For all m < 24 there are 2 or fewer solutions to bsigma(x) = m, thus 24 is in the sequence.

%t fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[b = bsigma[k]; If[b <= m, v[[b]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s

%Y Cf. A145899, A188999, A289132, A332036, A332037, A332039.

%K nonn

%O 1,2

%A _Amiram Eldar_, Feb 05 2020