A067663 Sequence gives values of gcd(k!+1, k^k-1) when not equal to 1 in order of appearance.

2, 3, 5, 11, 7, 19, 11, 13, 17, 19, 43, 23, 401, 29, 31, 67, 37, 41, 43, 47, 53, 59, 61, 131, 67, 71, 73, 79, 163, 83, 89, 179, 97, 101, 103, 107, 109, 113, 227, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 347, 179, 181, 191, 193, 197, 199, 419, 211, 443, 223

Offset

1,1

Comments

Sequence appears to contain each prime number once or twice.

Links

Table of n, a(n) for n=1..60.

Formula

For some even k: gcd(k!+1, k^k-1) = k+1;

for some odd k: gcd(k!+1, k^k-1) = 2*k+1.

Example

For k=25, gcd(k!+1, k^k-1) = 401;
for k=788, gcd(k!+1, k^k-1) = 4729.

Maple

select(x-> x>1, [seq(igcd(k!+1, k^k-1), k=1..300)])[];  # Alois P. Heinz, Oct 26 2019

Crossrefs

Sequence in context: A084331 A084333 A288833 * A112037 A087583 A372284

Adjacent sequences: A067660 A067661 A067662 * A067664 A067665 A067666

Keyword

nonn

Author

Benoit Cloitre, Feb 03 2002

Status

approved