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A187730 Greatest common divisor of Carmichael lambda(n) and n - 1. 8

%I #26 Oct 11 2019 16:53:20

%S 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,

%T 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,

%U 2,1,4,5,66,1,2,3,70,1,72,1,2,3,2,1,78,1

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

%C 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).

%H Amiram Eldar, <a href="/A187730/b187730.txt">Table of n, a(n) for n = 1..10000</a>

%H J. M. Grau and Antonio Oller-Marcén, <a href="http://arxiv.org/abs/1103.3483">Generalizing Giuga's conjecture</a>, arXiv:1103.3483 [math.NT], 2011.

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

%o (PARI) a(n) = gcd(lcm(znstar(n)[2]), n-1); \\ _Michel Marcus_, Mar 18 2016

%Y Cf. A002322 (Carmichael lambda function).

%K nonn

%O 1,3

%A _José María Grau Ribas_, Mar 13 2011

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)