This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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