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A366027
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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.
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2
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1, 2, 4, 3, 16, 5, 64, 8, 256, 17, 1024, 6, 4096, 65, 20, 9, 65536, 7, 262144, 10, 68, 1025, 4194304, 11, 16777216, 4097, 257, 66, 268435456, 18, 1073741824, 128, 1028, 65537, 80, 12, 68719476736, 262145, 4100, 19, 1099511627776, 32, 4398046511104, 1026, 21
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OFFSET
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1,2
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COMMENTS
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In other words, the binary expansion of a(n) encodes a subset of the divisors of n.
This sequence is a permutation of the positive integers with inverse A366028.
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LINKS
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FORMULA
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a(p) = 2^(p-1) for any prime number p.
a(2*p) = 2^(p-1) + 1 for any prime number p.
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EXAMPLE
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The first terms, alongside their binary expansion and the corresponding divisors d, are:
n a(n) bin(a(n)) Corresponding divisors
-- ------ ------------------- ----------------------
1 1 1 {1}
2 2 10 {2}
3 4 100 {3}
4 3 11 {2, 1}
5 16 10000 {5}
6 5 101 {3, 1}
7 64 1000000 {7}
8 8 1000 {4}
9 256 100000000 {9}
10 17 10001 {5, 1}
11 1024 10000000000 {11}
12 6 110 {3, 2}
13 4096 1000000000000 {13}
14 65 1000001 {7, 1}
15 20 10100 {5, 3}
16 9 1001 {4, 1}
17 65536 10000000000000000 {17}
18 7 111 {3, 2, 1}
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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