A339345 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.

1, 3, 5, 9, 15, 17, 25, 27, 45, 51, 75, 81, 85, 125, 135, 153, 225, 243, 255, 257, 289, 375, 405, 425, 459, 625, 675, 729, 765, 771, 867, 1125, 1215, 1275, 1285, 1377, 1445, 1875, 2025, 2125, 2187, 2295, 2313, 2601, 3125, 3375, 3645, 3825, 3855, 4131, 4335, 4369

Offset: 1

Author

Amiram Eldar, Nov 30 2020

Keywords

• nonn

Comments

Numbers whose prime divisors are all in A339344.

Closed under multiplication.

First differs from A143512 and A174688 at n = 970.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A143512, A174688, A339344.

Programs

Mathematica

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]

Formula

Sum_{n>=1} 1/a(n) = 2.