%I
%S 1,2,4,6,3,9,12,8,10,5,15,25,20,16,14,7,21,27,18,24,30,32,22,11,33,66,
%T 36,42,28,49,35,70,40,50,60,45,75,81,39,13,26,52,64,34,17,51,102,48,
%U 54,72,78,96,84,56,98,112,126,63,105,125,55,110,44,88,121,77
%N a(1)=1, a(2) = 2; for n > 2, a(n) is the smallest number not already used such that the set of prime divisors of one of the numbers {a(n1), a(n)} is a subset of the set of prime divisors of the other.
%C The sequence is an analog of EKGsequence A064413 with more hard condition on neighbor terms. However, we conjecture that, as A064413, it is a permutation of the positive integers.
%C By the definition, every two neighbor terms are strictly connected numbers defined in comment in A257112.
%H Peter J. C. Moses, <a href="/A255348/b255348.txt">Table of n, a(n) for n = 1..5000</a>
%Y Cf. A064413, A257112.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, May 05 2015
%E More terms from _Peter J. C. Moses_, May 05 2015
