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A366027 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, if 2^(d-1) appears in the binary expansion of a(n) then d divides n.

%I A366027 #6 Oct 02 2023 13:49:00
%S A366027 1,2,4,3,16,5,64,8,256,17,1024,6,4096,65,20,9,65536,7,262144,10,68,
%T A366027 1025,4194304,11,16777216,4097,257,66,268435456,18,1073741824,128,
%U A366027 1028,65537,80,12,68719476736,262145,4100,19,1099511627776,32,4398046511104,1026,21
%N A366027 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, if 2^(d-1) appears in the binary expansion of a(n) then d divides n.
%C A366027 In other words, the binary expansion of a(n) encodes a subset of the divisors of n.
%C A366027 This sequence is a permutation of the positive integers with inverse A366028.
%H A366027 Rémy Sigrist, <a href="/A366027/a366027.gp.txt">PARI program</a>
%H A366027 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A366027 a(p) = 2^(p-1) for any prime number p.
%F A366027 a(2*p) = 2^(p-1) + 1 for any prime number p.
%e A366027 The first terms, alongside their binary expansion and the corresponding divisors d, are:
%e A366027   n   a(n)    bin(a(n))            Corresponding divisors
%e A366027   --  ------  -------------------  ----------------------
%e A366027    1       1                    1  {1}
%e A366027    2       2                   10  {2}
%e A366027    3       4                  100  {3}
%e A366027    4       3                   11  {2, 1}
%e A366027    5      16                10000  {5}
%e A366027    6       5                  101  {3, 1}
%e A366027    7      64              1000000  {7}
%e A366027    8       8                 1000  {4}
%e A366027    9     256            100000000  {9}
%e A366027   10      17                10001  {5, 1}
%e A366027   11    1024          10000000000  {11}
%e A366027   12       6                  110  {3, 2}
%e A366027   13    4096        1000000000000  {13}
%e A366027   14      65              1000001  {7, 1}
%e A366027   15      20                10100  {5, 3}
%e A366027   16       9                 1001  {4, 1}
%e A366027   17   65536    10000000000000000  {17}
%e A366027   18       7                  111  {3, 2, 1}
%o A366027 (PARI) See Links section.
%Y A366027 Cf. A048793, A271410, A366028 (inverse).
%K A366027 nonn,base
%O A366027 1,2
%A A366027 _Rémy Sigrist_, Sep 26 2023