A292984 Bi-unitary superabundant numbers: numbers n such that bsigma(n)/n > bsigma(m)/m for all m < n, where bsigma is the sum of the bi-unitary divisors function (A188999).

1, 2, 6, 24, 96, 120, 480, 840, 3360, 7560, 30240, 83160, 332640, 1081080, 4324320, 17297280, 69189120, 73513440, 294053760, 1176215040, 1396755360, 5587021440

Offset

1,2

Comments

Analogous to superabundant numbers (A004394) with bi-unitary sigma (A188999) instead of sigma (A000203).

The least bi-unitary k-abundant number (bsigma(m)/m > k*m) for k = 1, 2, ... is 1, 24, 480, 83160, 294053760. - Amiram Eldar, Dec 05 2018

Links

Table of n, a(n) for n=1..22.

Mathematica

fun[p_, e_]:=If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[n_] := If[n==1, 1, Times @@ (fun @@@ FactorInteger[n])]; a = {}; rmax = 0; Do[r = bsigma[n]/n; If[r > rmax, AppendTo[a, n]; rmax = r], {n, 1000}]; a

Crossrefs

Cf. A004394, A188999.

Sequence in context: A376810 A115220 A293185 * A072854 A147944 A147935

Adjacent sequences: A292981 A292982 A292983 * A292985 A292986 A292987

Keyword

nonn,more

Author

Amiram Eldar, Sep 27 2017

Extensions

a(14)-a(22) from Amiram Eldar, Dec 06 2018

Status

approved