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%I #28 May 14 2019 08:07:30
%S 1,2,6,24,96,120,480,840,3360,7560,30240,83160,272160,332640,1081080,
%T 2993760,4324320,17297280,38918880,69189120,73513440,294053760,
%U 661620960,1176215040,1396755360,5587021440,12570798240,22348085760,32125373280,128501493120
%N Bi-unitary highly composite numbers: where the number of bi-unitary divisors of n (A286324) increases to a record.
%C Analogous to highly composite numbers (A002182) with number of bi-unitary divisors (A286324) instead of number of divisors (A000005).
%C The first 12 terms are common with bi-unitary superabundant numbers (A292984).
%C The record numbers of bi-unitary divisors are 1, 2, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 144, 192, 256, 288, 384, ... (see the link for more values).
%H Amiram Eldar, <a href="/A293185/b293185.txt">Table of n, a(n) for n = 1..122</a>
%H Amiram Eldar, <a href="/A293185/a293185_1.txt">Table of n, a(n), A286324(a(n)) for n = 1..122</a>
%t f[p_, e_] := If[OddQ[e], (e + 1), e]; bdivnum[n_] := If[n == 1, 1, Times @@ (f @@@ FactorInteger[n])]; bm = 0; s = {}; Do[b1 = bdivnum [k]; If[b1 > bm, AppendTo[s, k]; bm = b1], {k, 1, 100000}]; s
%Y Cf. A002182, A286324, A292984.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 01 2017
%E a(18)-a(30) from _Amiram Eldar_, Dec 01 2018
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