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