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A049586 a(n) is the GCD of the cototients (A051953) of n and n+1.

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%I A049586 #23 Sep 08 2022 08:44:58
%S A049586 1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A049586 1,1,1,5,3,1,1,1,1,3,3,1,1,1,1,1,1,1,1,3,1,1,3,1,1,1,1,1,1,1,1,1,1,1,
%U A049586 1,1,1,1,1,1,5,1,1,1,1,3,3,1,1,3,1,1,1,1,1,1,1,3,3,1,1,1,1,1,3,1,1,1,1,1,3
%N A049586 a(n) is the GCD of the cototients (A051953) of n and n+1.
%C A049586 Most of the terms are 1.
%H A049586 Vincenzo Librandi, <a href="/A049586/b049586.txt">Table of n, a(n) for n = 0..5000</a>
%F A049586 a(n) = gcd(n + 1 - phi(n+1), n - phi(n)).
%F A049586 a(n) = gcd(A051953(n+1), A051953(n)).
%t A049586 Map[GCD @@ Map[# - EulerPhi@ # &, #] &, Partition[Range@ 106, 2, 1]] (* _Michael De Vlieger_, Aug 09 2017 *)
%o A049586 (Magma) [GCD((n+1-EulerPhi(n+1)), n-EulerPhi(n)): n in [1..100]]; // _Vincenzo Librandi_, Aug 10 2017
%Y A049586 Cf. A000010, A051953, A058515.
%K A049586 nonn
%O A049586 0,9
%A A049586 _Labos Elemer_, Dec 28 2000