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A201560 a(n) = (Sum(m^(n-1), m=1..n-1) + 1) modulo n. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A097898 A154884 A334385 * A255644 A059678 A079642

Adjacent sequences:  A201557 A201558 A201559 * A201561 A201562 A201563

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Jan 11 2012

STATUS

approved

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Last modified May 30 18:07 EDT 2020. Contains 334728 sequences. (Running on oeis4.)