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

Author

Amiram Eldar, Oct 01 2017

Keywords

• nonn

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

Crossrefs

Cf. A002182, A286324, A292984.

Programs

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

Extensions

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