A235363 (1 + Sum_{k=1..m-1} k^(m-1)) (mod m), for m = 1, 3, 5, 7, 9, ...

0, 0, 0, 0, 7, 0, 0, 11, 0, 0, 15, 0, 21, 19, 0, 0, 23, 1, 0, 27, 0, 0, 22, 0, 43, 35, 0, 1, 39, 0, 0, 43, 53, 0, 47, 0, 0, 51, 1, 0, 55, 0, 69, 59, 0, 79, 63, 1, 0, 67, 0, 0, 50, 0, 0, 75, 0, 1, 79, 1, 111, 83, 101, 0, 87, 0, 115, 91, 0, 0, 95, 1, 117, 99, 0, 0, 103, 1, 0, 107, 1, 0, 78, 0, 157, 115, 0, 151, 119, 0, 0, 123, 149, 1, 127, 0, 0, 131, 0, 0, 135

Offset: 0

Author

Jonathan Sondow, Jan 07 2014

Keywords

• nonn

Comments

a(n) = (1 + Sum_{k=1..2*n} k^(2*n)) (mod 2*n+1), for n = 0, 1, 2, 3, ...

The Agoh-Giuga Conjecture is that a(n)=0 iff 2*n+1 is 1 or a prime.

Links

• MathWorld, Giuga's Conjecture
• Wikipedia, Agoh-Giuga conjecture

Crossrefs

Cf. A007850, A046094, A204187, A228037, A235364.

Programs

Mathematica

Table[ Mod[ Sum[ PowerMod[ k, n - 1, n], {k, n - 1}] + 1, n], {n, 1, 201, 2}]

Formula

a(n) = 0 iff A235364(n) = 0.