A181569 Greatest common divisor of n! and n+1.

1, 1, 2, 1, 6, 1, 8, 9, 10, 1, 12, 1, 14, 15, 16, 1, 18, 1, 20, 21, 22, 1, 24, 25, 26, 27, 28, 1, 30, 1, 32, 33, 34, 35, 36, 1, 38, 39, 40, 1, 42, 1, 44, 45, 46, 1, 48, 49, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 60, 1, 62, 63, 64, 65, 66, 1, 68, 69, 70, 1, 72, 1, 74, 75, 76, 77, 78, 1

Offset: 1

Author

Reinhard Zumkeller, Oct 31 2010

Keywords

• nonn
• easy

Comments

From Wilson's theorem, it follows that a(n) = 1 when n + 1 is prime, a(n) > 1 otherwise. - Alonso del Arte, Feb 25 2014

Examples

			a(6) = 1 because 6! and 7 are coprime.
a(7) = 8 because 7! = 5040 and gcd(5040, 8) = 8.
a(8) = 9 because 8! = 40320 and gcd(40320, 9) = 9.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000142, A006093, A010051, A050873.

Cf. A088140, A135683.

Programs

Magma

[GCD(Factorial(n), n+1): n in [1..80]]; // Vincenzo Librandi, Mar 03 2014

Maple

A181569:=n->gcd(n!,n+1): seq(A181569(n), n=1..100); # Wesley Ivan Hurt, Aug 13 2015

Mathematica

Table[GCD[n!, n + 1], {n, 80}] (* Alonso del Arte, Feb 25 2014 *)

PARI

a(n)= n!/denominator(polcoeff((x+1)*exp(x+x*O(x^n)), n));  \\ Gerry Martens, Aug 12 2015

PARI

A181569(n)=gcd(n!,n+1) \\ M. F. Hasler, Aug 16 2015

Formula

a(n) = A050873(A000142(n), n + 1);

a(A006093(n)) = 1;

for n > 3: a(n) = (n + 1) / (n*A010051(n+1) + 1).

a(n) = (n+1)/A014973(n+1). - Michel Marcus, Aug 14 2015