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%I #16 Mar 22 2020 09:57:51
%S 1,2,3,2,5,2,7,2,9,2,11,12,13,2,15,2,17,2,19,4,21,2,23,4,25,2,27,4,29,
%T 30,31,2,33,2,35,12,37,2,39,20,41,6,43,4,45,2,47,12,49,2,51,4,53,2,55,
%U 56,57,2,59,4,61,2,63,2,65,6,67,4,69,14,71,4,73,2,75,4,77,2,79,20,81,2
%N a(n) = gcd(n,binomial(n,floor(n/2))).
%C For even n, a(n) is an even divisor of n.
%H Hugo Pfoertner, <a href="/A057815/b057815.txt">Table of n, a(n) for n = 1..10000</a>
%F a(2k+1) = 2k+1. a(2k) = A058005(k).
%p swing := n -> n!/iquo(n,2)!^2: seq(igcd(n,swing(n)), n=1..82); # _Peter Luschny_, May 17 2013
%t a[n_] := GCD[n, Binomial[n, Floor[n/2]]]; Array[a, 100] (* _Jean-François Alcover_, Jun 03 2019 *)
%o (PARI) a(n) = gcd(n,binomial(n, n\2)); \\ _Michel Marcus_, Mar 22 2020
%Y Cf. A001405, A049077.
%K nonn
%O 1,2
%A _Labos Elemer_, Nov 13 2000
%E Offset changed to 1 by _Peter Luschny_, May 17 2013
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