A127992 Number of distinct prime factors of 2*n^3 - 2*n + 9.

1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 4, 2, 3, 3, 3, 3, 3, 3, 2, 4, 3, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 4, 3, 4, 3, 2, 2, 3, 2, 2, 4, 2, 3, 4, 3, 3, 3, 4, 3, 2, 2, 2, 3, 3, 4, 3, 3, 4, 3, 3, 4, 4, 2, 2, 2, 3, 3, 3, 4, 3, 4, 2, 3, 2, 2, 3, 3, 3, 2, 4, 3, 2, 3, 4, 2, 3, 2, 4

Offset: 1

Author

Artur Jasinski, Feb 10 2007

Keywords

• nonn

Comments

All numbers generated by the irreducible polynomial 2n^3 - 2n + 9 (A127989) are odd multiples of 3.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A127989, A127990 (largest prime factor), A127992 (number of prime factors).

Programs

Mathematica

a = {}; Do[AppendTo[a, 2n^3 - 2n + 9], {n, 1, 300}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = Length[c]; AppendTo[b, d], {n, 1, Length[a]}]; b
Table[PrimeNu[2n^3-2n+9],{n,120}] (* Harvey P. Dale, Sep 24 2021 *)

PARI

a(n)=omega(2*n^3 - 2*n + 9) \\ Charles R Greathouse IV, Mar 13 2020

Formula

a(n) = A001221(A127989(n)). - Amiram Eldar, Mar 13 2020