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

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, 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, 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

Offset: 0

Author

Labos Elemer, Dec 28 2000

Keywords

• nonn

Comments

Most of the terms are 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000010, A051953, A058515.

Programs

Magma

[GCD((n+1-EulerPhi(n+1)), n-EulerPhi(n)): n in [1..100]]; // Vincenzo Librandi, Aug 10 2017

Mathematica

Map[GCD @@ Map[# - EulerPhi@ # &, #] &, Partition[Range@ 106, 2, 1]] (* Michael De Vlieger, Aug 09 2017 *)

Formula

a(n) = gcd(n + 1 - phi(n+1), n - phi(n)).

a(n) = gcd(A051953(n+1), A051953(n)).