A302571 Bi-unitary barely abundant numbers: bi-unitary abundant numbers k such that bsigma(k)/k < bsigma(m)/m for all bi-unitary abundant numbers m < k, where bsigma(k) is the sum of the bi-unitary divisors of k (A188999).

24, 30, 40, 54, 56, 70, 80, 104, 642, 654, 678, 726, 762, 786, 822, 832, 1888, 1952, 4030, 5830, 7424, 32128, 62464, 374802, 374838, 374862, 374898, 374982, 375006, 375042, 375198, 375234, 375294, 375378, 375486, 375546, 375582, 375618, 375702, 375762, 375798

Offset: 1

Author

Amiram Eldar, Apr 10 2018

Keywords

• nonn

Examples

			The values of bsigma(k)/k are: 3, 2.5, 2.4, 2.25, 2.222..., 2.142...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The bi-unitary version of A071927.

Cf. A188999, A292982, A302570.

Programs

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=  DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; r = 3; seq={}; Do[
s = bsigma[n]/n; If[s > 2 && s < r, AppendTo[seq,n]; r = s], {n, 1, 10000}]; seq

PARI

babindex(n) = {my(f = factor(n), p, e); prod(k = 1, #f~, p = f[k, 1]; e = f[k, 2]; (p^(e+1)-1)/(p^(e+1)-p^e) - if(e%2, 0, 1/p^(e/2)));}
lista(kmax) = {my(bab, babm = 3); for(k = 1, kmax, bab = babindex(k); if(bab > 2 && bab < babm, babm = bab; print1(k, ", "))); }