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%I #18 Oct 22 2023 15:06:10
%S 1,1,1,2,1,1,1,2,3,1,1,1,1,1,1,2,1,3,1,1,1,1,1,1,5,1,3,1,1,1,1,2,1,1,
%T 1,3,1,1,1,1,1,1,1,1,3,1,1,1,7,5,1,1,1,3,1,1,1,1,1,1,1,1,1,2,1,1,1,1,
%U 1,1,1,3,1,1,5,1,1,1,1,1,3,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,7,3,5
%N a(n) = gcd(n, phi(n)^2) / gcd(n, phi(n)).
%C a(n) = 1 if n is squarefree.
%H Paolo Xausa, <a href="/A362414/b362414.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = gcd(n,A127473(n)) / A009195(n).
%F 1 <= a(n) <= sqrt(n). The lower bound is sharp (squarefree numbers), as is the upper bound (squares of primes). - _Charles R Greathouse IV_, May 03 2023
%t A362414[n_]:=With[{p=EulerPhi[n]},GCD[n,p^2]/GCD[n,p]];
%t Array[A362414,100] (* _Paolo Xausa_, Oct 22 2023 *)
%o (Magma) [Gcd(n, EulerPhi(n)^2) / Gcd(n, EulerPhi(n)): n in [1..100]];
%o (PARI) a(n)=my(f=eulerphi(n)); gcd(n,f^2)/gcd(n,f) \\ _Charles R Greathouse IV_, May 03 2023
%Y Cf. A000010, A000188, A009195.
%K nonn,easy
%O 1,4
%A _Juri-Stepan Gerasimov_, Apr 19 2023
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