cp's OEIS Frontend

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).

%I A302571 #19 Mar 26 2023 02:21:30
%S A302571 24,30,40,54,56,70,80,104,642,654,678,726,762,786,822,832,1888,1952,
%T A302571 4030,5830,7424,32128,62464,374802,374838,374862,374898,374982,375006,
%U A302571 375042,375198,375234,375294,375378,375486,375546,375582,375618,375702,375762,375798
%N 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).
%H A302571 Amiram Eldar, <a href="/A302571/b302571.txt">Table of n, a(n) for n = 1..10000</a>
%e A302571 The values of bsigma(k)/k are: 3, 2.5, 2.4, 2.25, 2.222..., 2.142...
%t A302571 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[
%t A302571 s = bsigma[n]/n; If[s > 2 && s < r, AppendTo[seq,n]; r = s], {n, 1, 10000}]; seq
%o A302571 (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)));}
%o A302571 lista(kmax) = {my(bab, babm = 3); for(k = 1, kmax, bab = babindex(k); if(bab > 2 && bab < babm, babm = bab; print1(k, ", "))); }
%Y A302571 The bi-unitary version of A071927.
%Y A302571 Cf. A188999, A292982, A302570.
%K A302571 nonn
%O A302571 1,1
%A A302571 _Amiram Eldar_, Apr 10 2018