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A362414
a(n) = gcd(n, phi(n)^2) / gcd(n, phi(n)).
1
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, 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, 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
OFFSET
1,4
COMMENTS
a(n) = 1 if n is squarefree.
FORMULA
a(n) = gcd(n,A127473(n)) / A009195(n).
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
MATHEMATICA
A362414[n_]:=With[{p=EulerPhi[n]}, GCD[n, p^2]/GCD[n, p]];
Array[A362414, 100] (* Paolo Xausa, Oct 22 2023 *)
PROG
(Magma) [Gcd(n, EulerPhi(n)^2) / Gcd(n, EulerPhi(n)): n in [1..100]];
(PARI) a(n)=my(f=eulerphi(n)); gcd(n, f^2)/gcd(n, f) \\ Charles R Greathouse IV, May 03 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved