A293185 Bi-unitary highly composite numbers: where the number of bi-unitary divisors of n (A286324) increases to a record.

1, 2, 6, 24, 96, 120, 480, 840, 3360, 7560, 30240, 83160, 272160, 332640, 1081080, 2993760, 4324320, 17297280, 38918880, 69189120, 73513440, 294053760, 661620960, 1176215040, 1396755360, 5587021440, 12570798240, 22348085760, 32125373280, 128501493120

Offset

1,2

Comments

Analogous to highly composite numbers (A002182) with number of bi-unitary divisors (A286324) instead of number of divisors (A000005).

The first 12 terms are common with bi-unitary superabundant numbers (A292984).

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..122

Amiram Eldar, Table of n, a(n), A286324(a(n)) for n = 1..122

Mathematica

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

Crossrefs

Cf. A002182, A286324, A292984.

Sequence in context: A367274 A361752 A115220 * A292984 A072854 A147944

Adjacent sequences: A293182 A293183 A293184 * A293186 A293187 A293188

Keyword

nonn

Author

Amiram Eldar, Oct 01 2017

Extensions

a(18)-a(30) from Amiram Eldar, Dec 01 2018

Status

approved