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

Author

Amiram Eldar, Sep 27 2017

Keywords

• nonn
• more

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

Crossrefs

Cf. A004394, A188999.

Programs

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

Extensions

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