A335053 - OEIS

A335053

Odd bi-unitary abundant numbers whose bi-unitary abundancy is closer to 2 than that of any smaller odd bi-unitary abundant number.

%I #7 May 21 2020 21:20:04

%S 945,25515,46035,49875,83265,354585,359205,361515,366135,382305,

%T 389235,396165,400785,403095,407715,414645,416955,423885,430815,

%U 437745,442365,13351635,132335385,159030135,1756753845,6561644355,10394173335,13455037365,37456183215

%N Odd bi-unitary abundant numbers whose bi-unitary abundancy is closer to 2 than that of any smaller odd bi-unitary abundant number.

%C The bi-unitary abundancy of a number k is bsigma(k)/k, where bsigma(k) is the sum of bi-unitary divisors of k (A188999).

%e The bi-unitary abundancies of the first terms are 2.031..., 2.005..., 2.0019..., 2.0018..., 2.0015..., ...

%t fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); seq = {}; r = 3; Do[s = bsigma[n]/n; If[s > 2 && s < r, AppendTo[seq, n]; r = s], {n, 1, 10^6, 2}]; seq

%Y Cf. A188999, A188263, A293186, A302571, A335052, A335055.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 21 2020