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%I #4 May 18 2020 19:58:00
%S 945,43065,46035,80535,354585,403095,430815,437745,442365,2305875,
%T 3525795,4404105,4891887,5388495,5927985,6126645,6220665,6375105,
%U 6537375,7853625,8109585,8731125,9071865,9338595,9784125,13241745,23760555,33381855,34592805,35642295
%N Odd infinitary admirable numbers: the odd terms of A334974.
%C Of the first 10^4 infinitary admirable numbers only 9 are odd.
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; infDivQ[n_, 1] = True; infDivQ[n_, d_] := BitAnd[IntegerExponent[n, First /@ (f = FactorInteger[d])], (e = Last /@ f)] == e; infAdmQ[n_] := (ab = isigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && infDivQ[n, ab/2]; Select[Range[1, 5*10^5, 2], infAdmQ]
%Y The infinitary version of A109729.
%Y Intersection of A005408 and A334974.
%Y Subsequence of A127666.
%Y Cf. A329188, A334973.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 18 2020
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