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A207790 Permutation of positive numbers. See comments.

%I A207790 #25 May 01 2016 03:29:24
%S A207790 1,2,4,3,8,5,6,7,16,11,9,13,12,17,10,19,32,23,14,29,18,31,15,37,24,41,
%T A207790 21,43,20,47,22,53,64,59,25,61,27,67,26,71,36,73,33,79,28,83,34,89,48,
%U A207790 97,35,101,30,103,38,107,40,109,39,113,42,127,46,131,128,137,49,139,44,149,51,151
%N A207790 Permutation of positive numbers. See comments.
%C A207790 a(1)=1; on places 2,4,6,8,... we put primes (A000040); on places 3,7,11,15,... we put products of two primes (A001358); on places 5,13,21,29,... we put products of three primes (A014612); on places 9,25,41,57,... we put products of four primes (A014613); on places 17,49,81,... we put products of five primes (A014614); etc.
%C A207790 Primes with the index not exceeding n have density 1/2, semiprimes have density 1/4, etc.
%C A207790 By our system, here and in  A207800, A207801, A207802 we used the order: a(1)=1; the first appearance  of a new kind of numbers in places of the form 2^k+1, k=0,1,2,..., with  period of the appearance 2^{k+1}.
%H A207790 Ivan Neretin, <a href="/A207790/b207790.txt">Table of n, a(n) for n = 1..8192</a>
%F A207790 For n>1, a(n) = A078840(A249725(n-1)). - _Ivan Neretin_, Apr 30 2016
%t A207790 mx = 72; a = Array[1 &, mx]; cnt = mx - 1; offs = Table[2^(i - 1) + 1, {i, 1, mx}]; n = 1; While[cnt > 0, n++; idx = PrimeOmega[n]; pos = offs[[idx]]; If[pos > mx, Continue[]]; offs[[idx]] += 2^idx; a[[pos]] = n; cnt--]; a (* _Ivan Neretin_, May 06 2015 *)
%Y A207790 Cf. A057114.
%K A207790 nonn
%O A207790 1,2
%A A207790 _Vladimir Shevelev_ and _Peter J. C. Moses_, Feb 20 2012