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%I A009194 #49 Feb 07 2024 01:16:00
%S A009194 1,1,1,1,1,6,1,1,1,2,1,4,1,2,3,1,1,3,1,2,1,2,1,12,1,2,1,28,1,6,1,1,3,
%T A009194 2,1,1,1,2,1,10,1,6,1,4,3,2,1,4,1,1,3,2,1,6,1,8,1,2,1,12,1,2,1,1,1,6,
%U A009194 1,2,3,2,1,3,1,2,1,4,1,6,1,2,1,2,1,28,1,2,3,4,1,18,7,4,1,2,5,12,1,1,3,1,1,6,1,2
%N A009194 a(n) = gcd(n, sigma(n)).
%C A009194 LCM of common divisors of n and sigma(n). It equals n if n is multiply perfect (A007691). - _Labos Elemer_, Aug 14 2002
%H A009194 Reinhard Zumkeller, <a href="/A009194/b009194.txt">Table of n, a(n) for n = 1..10000</a>
%H A009194 P. Pollack, <a href="http://projecteuclid.org/euclid.mmj/1301586311">On the greatest common divisor of a number and its sum of divisors</a>, Michigan Math. J. Volume 60, Issue 1 (2011), 199-214.
%F A009194 A000005(a(n)) = A073802(n). - _Reinhard Zumkeller_, Mar 12 2010
%F A009194 A006530(a(n)) = A082062(n). - _Reinhard Zumkeller_, Jul 10 2011
%F A009194 a(A014567(n)) = 1; A069059(a(n)) > 1. - _Reinhard Zumkeller_, Mar 23 2013
%F A009194 a(n) = n/A017666(n). - _Antti Karttunen_, May 22 2017
%t A009194 Table[GCD[n,DivisorSigma[1,n]],{n,110}] (* _Harvey P. Dale_, Aug 23 2015 *)
%o A009194 (Haskell)
%o A009194 a009194 n = gcd (a000203 n) n  -- _Reinhard Zumkeller_, Mar 23 2013
%o A009194 (PARI) a(n) = gcd(n, sigma(n)); \\ _Michel Marcus_, Oct 23 2013
%Y A009194 Cf. A000203, A003624, A007691, A014567, A017666, A063906, A069059, A073802, A082062, A179931, A205523, A216793 (positions of records), A234367, A249917.
%Y A009194 Cf. also A009191, A009205, A009242, A274382, A286591, A286594.
%K A009194 nonn
%O A009194 1,6
%A A009194 _David W. Wilson_

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