A292983 Bi-unitary highly abundant numbers: numbers n such that bsigma(n) > bsigma(m) for all m < n, where bsigma is the sum of the bi-unitary divisors function (A188999).

1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 22, 24, 30, 40, 42, 48, 54, 66, 72, 78, 88, 96, 120, 160, 168, 210, 216, 240, 264, 312, 330, 360, 378, 384, 408, 456, 480, 600, 648, 672, 840, 1056, 1080, 1320, 1512, 1560, 1680, 1848, 1920, 2040, 2184, 2280, 2640

Offset: 1

Author

Amiram Eldar, Sep 27 2017

Keywords

• nonn

Comments

Analogous to highly abundant numbers (A002093) with bi-unitary sigma (A188999) instead of sigma (A000203).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..569 (terms below 10^10)

Crossrefs

Cf. A002093, A188999, A285614.

Programs

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; a = {}; bmax = 0; Do[b = bsigma[n]; If[b > bmax, AppendTo[a, n]; bmax = b], {n, 3000}]; a (* after Michael De Vlieger at A188999 *)