A201560 a(n) = (Sum(m^(n-1), m=1..n-1) + 1) modulo n.

0, 0, 0, 1, 0, 4, 0, 1, 7, 6, 0, 1, 0, 8, 11, 1, 0, 10, 0, 1, 15, 12, 0, 1, 21, 14, 19, 1, 0, 16, 0, 1, 23, 18, 1, 1, 0, 20, 27, 1, 0, 22, 0, 1, 22, 24, 0, 1, 43, 26, 35, 1, 0, 28, 1, 1, 39, 30, 0, 1, 0, 32, 43, 1, 53, 34, 0, 1, 47, 36, 0, 1, 0, 38, 51, 1, 1

Offset: 1

Author

Jonathan Sondow, Jan 11 2012

Keywords

• nonn

Comments

Equals 0 if n is 1 or a prime, by Fermat's little theorem. It is conjectured that the converse is also true; see A055030, A055032, A204187 and note that a(n) = 0 <==> A055032(n) = 1 <==> A204187(n) = n-1.

Examples

			Sum(m^3, m=1..3) + 1 = 1^3 + 2^3 + 3^3 + 1 = 37 == 1 (mod 4), so a(4) = 1.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, A17.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055023, A055030, A055031, A055032, A204187.

Programs

Mathematica

Table[Mod[Plus @@ PowerMod[Range[n - 1], n - 1, n] + 1, n], {n, 77}] (* Ivan Neretin, Sep 23 2016 *)

Formula

a(prime) = 0 and a(4n) = 1.

a(n) == A204187(n) + 1 (mod n).