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A126025 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}.

%I A126025 #15 Aug 13 2015 08:24:19
%S A126025 1,3,9,26,106,191,954,2427,8404,15945,111952,141117,1176623,2270566,
%T A126025 4477947,10345290,104257447,145407966,1633452518,2517488363,
%U A126025 5024167821,9148333241,120260250853
%N A126025 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}.
%C A126025 The greatest common divisor condition was suggested by A061446.
%H A126025 Manfred Scheucher, <a href="/A126025/a126025.sage.txt">Sage Script</a>
%H A126025 Manfred Scheucher, <a href="/A126025/a126025.c.txt">C Code</a>
%o A126025 (Haskell)
%o A126025 a126025 n = h n1s 0 where
%o A126025    h us c = if us == nns then c + 1 else h (succ us) (c + g) where
%o A126025      g = if and [f x `gcd` f y == f (x `gcd` y) |
%o A126025                  x <- [1 .. n - 1], y <- [x + 1 .. n]] then 1 else 0
%o A126025      f = (us !!) . subtract 1
%o A126025    succ (z:zs) = if z < n then (z + 1) : zs else 1 : succ zs
%o A126025    n1s = take n [1, 1 ..]; nns = take n [n, n ..]
%o A126025 -- _Reinhard Zumkeller_, May 04 2014
%Y A126025 Cf. A061446.
%Y A126025 Cf. A000312.
%K A126025 nonn,more,nice
%O A126025 1,2
%A A126025 _John W. Layman_, Feb 27 2007
%E A126025 a(10)-a(22) from _Manfred Scheucher_, Jun 06 2015
%E A126025 a(23) from _Manfred Scheucher_, Aug 13 2015