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%I #8 Dec 01 2020 02:52:21
%S 1,3,5,9,15,17,25,27,45,51,75,81,85,125,135,153,225,243,255,257,289,
%T 375,405,425,459,625,675,729,765,771,867,1125,1215,1275,1285,1377,
%U 1445,1875,2025,2125,2187,2295,2313,2601,3125,3375,3645,3825,3855,4131,4335,4369
%N Lexicographically earliest sequence of odd numbers such that the asymptotic density of the numbers which are coprime to all the terms of this sequence is 1/2.
%C Numbers whose prime divisors are all in A339344.
%C Closed under multiplication.
%C First differs from A143512 and A174688 at n = 970.
%H Amiram Eldar, <a href="/A339345/b339345.txt">Table of n, a(n) for n = 1..10000</a>
%F Sum_{n>=1} 1/a(n) = 2.
%t seq[m_] := Module[{v = {1}, r = 1, p = 3, k, n = m + 1, s = {1}, v1, s1, s2, rmax}, Do[AppendTo[v, p]; r *= 1 - 1/p; p = NextPrime[r/(r - 1/2)], {m}]; vmax = v[[-1]]; Do[v1 = v[[k]]; rmax = Floor[Log[vmax]/Log[v1]]; s1 = v1^Range[0, rmax]; s2 = Select[Union[Flatten[Outer[Times, s, s1]]], # <= vmax &]; s = Union[s, s2], {k, 2, n}]; s]; seq[5]
%Y Cf. A143512, A174688, A339344.
%K nonn
%O 1,2
%A _Amiram Eldar_, Nov 30 2020
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