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%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