A187730 Greatest common divisor of Carmichael lambda(n) and n - 1.

1, 1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 2, 1, 16, 1, 18, 1, 2, 1, 22, 1, 4, 1, 2, 3, 28, 1, 30, 1, 2, 1, 2, 1, 36, 1, 2, 1, 40, 1, 42, 1, 4, 1, 46, 1, 6, 1, 2, 3, 52, 1, 2, 1, 2, 1, 58, 1, 60, 1, 2, 1, 4, 5, 66, 1, 2, 3, 70, 1, 72, 1, 2, 3, 2, 1, 78, 1

Offset: 1

Author

José María Grau Ribas, Mar 13 2011

Keywords

• nonn

Comments

n is a Giuga number and A002322(n)/a(n) divides k if and only if 1^(k*(n-1)) + 2^(k*(n-1)) +...+ (n-1)^(k*(n-1)) = -1 (mod n).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• J. M. Grau and Antonio Oller-Marcén, Generalizing Giuga's conjecture, arXiv:1103.3483 [math.NT], 2011.

Crossrefs

Cf. A002322 (Carmichael lambda function).

Programs

Mathematica

Table[GCD[CarmichaelLambda[n],n-1],{n,100}]

PARI

a(n) = gcd(lcm(znstar(n)[2]), n-1); \\ Michel Marcus, Mar 18 2016