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A308176 Number of factors when x^3-x-1 is factorized mod the n-th prime. 1
1, 1, 2, 2, 2, 1, 2, 2, 3, 1, 1, 2, 1, 2, 1, 2, 3, 2, 2, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 2, 2, 1, 1, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 2, 1, 3, 1, 2, 2, 2, 3, 1, 2, 3, 1, 2, 3, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge, 1989; see page 131.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

EXAMPLE

The first few factorization are:

n, p, factors

1, 2, x^3+x+1

2, 3, x^3+2*x+2

3, 5, (x+3)*(x^2+2*x+3)

4, 7, (x+2)*(x^2+5*x+3)

5, 11, (x+5)*(x^2+6*x+2)

6, 13, x^3+12*x+12

7, 17, (x^2+5*x+7)*(x+12)

8, 19, (x^2+6*x+16)*(x+13)

9, 23, (x+20)*(x+13)^2

10, 29, x^3+28*x+28

11, 31, x^3+30*x+30

12, 37, (x^2+13*x+20)*(x+24)

...

MAPLE

p:=x^3-x-1;

f:=n->Factor(p) mod ithprime(n);

for n from 1 to 20 do lprint(n, ithprime(n), f(n)); od:

MATHEMATICA

a[n_] := Total[Last /@ FactorList[x^3-x-1, Modulus -> Prime[n]]] - 1; Array[a, 100] (* Giovanni Resta, May 28 2019 *)

PROG

(PARI) a(n) = vecsum(factor((x^3-x-1)*Mod(1, prime(n)))[, 2]); \\ Michel Marcus, May 28 2019

CROSSREFS

Sequence in context: A116858 A182134 A189684 * A106493 A309981 A083338

Adjacent sequences:  A308173 A308174 A308175 * A308177 A308178 A308179

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 26 2019

EXTENSIONS

More terms from Giovanni Resta, May 28 2019

STATUS

approved

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Last modified October 19 23:41 EDT 2019. Contains 328244 sequences. (Running on oeis4.)