A362414 a(n) = gcd(n, phi(n)^2) / gcd(n, phi(n)).

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

Author

Juri-Stepan Gerasimov, Apr 19 2023

Keywords

• nonn
• easy

Comments

a(n) = 1 if n is squarefree.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000188, A009195.

Programs

Magma

[Gcd(n, EulerPhi(n)^2) / Gcd(n, EulerPhi(n)): n in [1..100]];

Mathematica

A362414[n_]:=With[{p=EulerPhi[n]},GCD[n,p^2]/GCD[n,p]];
Array[A362414,100] (* Paolo Xausa, Oct 22 2023 *)

PARI

a(n)=my(f=eulerphi(n)); gcd(n,f^2)/gcd(n,f) \\ Charles R Greathouse IV, May 03 2023

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