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

1,2

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)

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 *)

Crossrefs

Cf. A002093, A188999, A285614.

Sequence in context: A120370 A011866 A321152 * A174709 A008724 A287642

Adjacent sequences: A292980 A292981 A292982 * A292984 A292985 A292986

Keyword

nonn

Author

Amiram Eldar, Sep 27 2017

Status

approved