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

1,6

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.

References

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

Links

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

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A154884 A338813 A334385 * A255644 A355174 A059678

Adjacent sequences: A201557 A201558 A201559 * A201561 A201562 A201563

Keyword

nonn

Author

Jonathan Sondow, Jan 11 2012

Status

approved