A263022 a(n) = gcd(n, 1^(n-1) + 2^(n-1) + ... + (n-1)^(n-1)) for n > 1.

1, 1, 4, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 5, 16, 1, 9, 1, 20, 7, 11, 1, 24, 5, 13, 9, 28, 1, 15, 1, 32, 11, 17, 35, 36, 1, 19, 13, 40, 1, 21, 1, 44, 3, 23, 1, 48, 7, 25, 17, 52, 1, 27, 55, 56, 19, 29, 1, 60, 1, 31, 21, 64, 13, 33, 1, 68, 23, 35, 1, 72, 1, 37, 25, 76, 77, 39, 1, 80, 27, 41, 1, 84, 17, 43, 29, 88, 1, 45, 13, 92, 31, 47, 95, 96

Offset: 2

Author

Thomas Ordowski, Oct 07 2015

Keywords

• nonn

Comments

a(n) = 1 if and only if n is a prime or n is a Carmichael number.

a(n) is divisible by 4 if n is divisible by 4, otherwise a(n) is odd. - Robert Israel, Oct 08 2015

a(n) = n iff 4|n or n = 35, 55, 77, 95; A121707 ?

a(5005) = 11: this is the first case where a(n) is prime and A001222(n) > 3. - Altug Alkan, Oct 08 2015

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A002997 (see my Oct 09 2013 comment).

Programs

Maple

f:= n -> igcd(n, add(j &^(n-1) mod n, j=1..n-1)):
seq(f(n), n=2..1000); # Robert Israel, Oct 08 2015

Mathematica

Table[GCD[n, Total@ Map[#^(n - 1) &, Range[n - 1]]], {n, 2, 96}] (* Michael De Vlieger, Oct 08 2015 *)

PARI

vector(100, n, gcd(n+1, sum(k=1, n, k^n))) \\ Altug Alkan, Oct 08 2015

Formula

a(4n) = 4n.

a(n) = gcd(A031971(n-1), n). - Michel Marcus, Oct 08 2015