A058515 GCD of totients of consecutive integers.

1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 2, 8, 8, 2, 6, 2, 4, 2, 2, 2, 4, 4, 6, 6, 4, 4, 2, 2, 4, 4, 8, 12, 12, 18, 6, 8, 8, 4, 6, 2, 4, 2, 2, 2, 2, 2, 4, 8, 4, 2, 2, 8, 12, 4, 2, 2, 4, 30, 6, 4, 16, 4, 2, 2, 4, 4, 2, 2, 24, 36, 4, 4, 12, 12, 6, 2, 2, 2, 2, 2, 8, 2, 14, 8, 8, 8, 24, 4, 4, 2, 2, 8, 32, 6

Offset: 1

Author

Labos Elemer, Dec 21 2000

Keywords

• nonn
• easy

Examples

			For n = 61, gcd(phi(62), phi(61)) = gcd(30, 60) = 30, so a(61) = 30.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A049586, A060778, A066813, A083542.

Programs

Mathematica

Map[GCD @@ # &, Partition[EulerPhi@ Range@ 98, 2, 1]] (* Michael De Vlieger, Aug 22 2017 *)

PARI

a(n) = gcd(eulerphi(n), eulerphi(n+1)); \\ Michel Marcus, Dec 10 2013

Formula

a(n) = gcd(phi(n+1), phi(n)), where phi = A000010.

a(n) = A083542(n)/A066813(n). - Amiram Eldar, May 07 2025

Extensions

Offset corrected to 1 by Michel Marcus, Dec 10 2013