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%I #5 May 18 2020 19:57:47
%S 945,43065,46035,48195,80535,354585,403095,430815,437745,442365,
%T 458055,2305875,3525795,4404105,4891887,5388495,5803245,6126645,
%U 6220665,6375105,6537375,7853625,7981875,8109585,8731125,9071865,9338595,9784125,13241745,13351635,23760555
%N Odd bi-unitary admirable numbers: the odd terms of A334972.
%C Of the first 10^4 bi-unitary admirable numbers only 11 are odd.
%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]); buDivQ[n_, 1] = True; buDivQ[n_, div_] := If[Mod[#2, #1] == 0, Last@Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; buAdmQ[n_] := (ab = bsigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && buDivQ[n, ab/2]; Select[Range[1, 5*10^5, 2], buAdmQ]
%Y The bi-unitary version of A109729.
%Y Intersection of A005408 and A334972.
%Y Subsequence of A293186.
%Y Cf. A329188, A334975.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 18 2020
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