A058665 a(n) = gcd(n+1, n-phi(n)).

2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1

Offset: 1

Author

Labos Elemer, Dec 28 2000

Keywords

• nonn

Comments

a(n) = 1 for most n. True for all primes and other integers.

Examples

			n = 247 = 13*19, n+1 = 248 = 8*31, phi(247) = 12*18 = 216, cototient(247) = 247-216 = 31, so a(247) = gcd(248,31) = 31.
		

Links

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

Crossrefs

Cf. A000010, A051953, A009195.

Programs

Mathematica

Table[GCD[n+1,n-EulerPhi[n]],{n,0,110}] (* Harvey P. Dale, Dec 24 2012 *)

PARI

A058665(n) = gcd(n+1, n-eulerphi(n)); \\ Antti Karttunen, Jul 28 2017

Python

from sympy import gcd, totient
def a(n): return gcd(n + 1, n - totient(n))
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jul 29 2017

Formula

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

Extensions

Offset corrected by Antti Karttunen, Jul 28 2017