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A126025
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Number of mappings f:{1,2,3,...,n} -> {1,2,3,...,n} such that gcd(f(x),f(y)) = f(gcd(x,y)) for all x,y in {1,2,3,...,n}.
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2
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1, 3, 9, 26, 106, 191, 954, 2427, 8404, 15945, 111952, 141117, 1176623, 2270566, 4477947, 10345290, 104257447, 145407966, 1633452518, 2517488363, 5024167821, 9148333241, 120260250853
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OFFSET
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1,2
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COMMENTS
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The greatest common divisor condition was suggested by A061446.
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LINKS
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PROG
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(Haskell)
a126025 n = h n1s 0 where
h us c = if us == nns then c + 1 else h (succ us) (c + g) where
g = if and [f x `gcd` f y == f (x `gcd` y) |
x <- [1 .. n - 1], y <- [x + 1 .. n]] then 1 else 0
f = (us !!) . subtract 1
succ (z:zs) = if z < n then (z + 1) : zs else 1 : succ zs
n1s = take n [1, 1 ..]; nns = take n [n, n ..]
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CROSSREFS
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KEYWORD
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nonn,more,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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