login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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).
6

%I #18 Dec 06 2018 04:38:33

%S 1,2,6,24,96,120,480,840,3360,7560,30240,83160,332640,1081080,4324320,

%T 17297280,69189120,73513440,294053760,1176215040,1396755360,5587021440

%N 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).

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

%C 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

%t 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

%Y Cf. A004394, A188999.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Sep 27 2017

%E a(14)-a(22) from _Amiram Eldar_, Dec 06 2018