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A109465
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a(1)=1; for n>1, a(n) = smallest positive integer not among the earlier terms of the sequence that is divisible by a different number of distinct primes than a(n-1).
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6
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1, 2, 6, 3, 10, 4, 12, 5, 14, 7, 15, 8, 18, 9, 20, 11, 21, 13, 22, 16, 24, 17, 26, 19, 28, 23, 30, 25, 33, 27, 34, 29, 35, 31, 36, 32, 38, 37, 39, 41, 40, 42, 43, 44, 47, 45, 49, 46, 53, 48, 59, 50, 60, 51, 61, 52, 64, 54, 66, 55, 67, 56, 70, 57, 71, 58, 73, 62, 78, 63, 79, 65
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OFFSET
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1,2
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COMMENTS
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Sequence is a permutation of the positive integers.
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LINKS
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EXAMPLE
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Of the positive integers (4,5,7,8,9,10,11,...) not among the first 4 terms of the sequence, 10 is the smallest which is divisible by a different number of distinct primes than a(4) = 3. So a(5) = 10.
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MATHEMATICA
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a = {1}; Do[k = 2; While[Nand[FreeQ[a, k], PrimeNu[k] != PrimeNu[a[[i - 1]]]], k++]; AppendTo[a, k], {i, 2, 72}]; a (* Michael De Vlieger, Sep 28 2017 *)
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PROG
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(Haskell)
import Data.List (delete)
a109465 n = a109465_list !! (n-1)
a109465_list = f 1 [1..] where
f o xs = g xs where
g (z:zs) = if o' == o then g zs else z : f o' (delete z xs)
where o' = a001221 z
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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