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%I #22 Sep 02 2022 04:55:56
%S 945,8505,10395,12285,15015,16065,17955,19305,19635,21735,21945,23205,
%T 23625,25245,25515,25935,26565,27405,28215,28875,29295,29835,31185,
%U 31395,33345,33495,33915,34125,34155,34965,35805,36855,37125,38745,39585,40635,41055
%N Odd bi-unitary abundant numbers: odd numbers k such that bsigma(k) > 2*k, where bsigma is the sum of the bi-unitary divisors function (A188999).
%C Analogous to odd abundant numbers (A005231) with bi-unitary sigma (A188999) instead of sigma (A000203).
%C The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 1, 2, 82, 559, 6493, 61831, 642468, 6339347, 63112602, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00063... . - _Amiram Eldar_, Sep 02 2022
%H Amiram Eldar, <a href="/A293186/b293186.txt">Table of n, a(n) for n = 1..10000</a>
%e 945 is in the sequence since bsigma(945) = 1920 > 2*945.
%t f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=
%t DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bOddAbundantQ[n_] := OddQ[n] && bsigma[n] > 2 n; Select[Range[1000], bOddAbundantQ] (* after _Michael De Vlieger_ at A188999 *)
%o (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
%o gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
%o biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));
%o biusig(n) = vecsum(biudivs(n));
%o isok(n) = (n % 2) && (biusig(n) > 2*n); \\ _Michel Marcus_, Dec 15 2017
%Y Cf. A005231, A129485, A188999, A292982.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 01 2017
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