A240975 The number of distinct prime factors of n^3-1.

0, 1, 2, 2, 2, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 4, 2, 2, 3, 2, 3, 3, 4, 2, 4, 3, 3, 2, 4, 3, 4, 3, 2, 3, 4, 4, 4, 2, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 2, 4, 3, 4, 2, 4, 4, 3, 4, 3, 3, 5, 2, 4, 4, 3, 3, 5, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 5, 2

Offset: 1

Author

R. J. Mathar, Aug 05 2014

Keywords

• nonn
• easy

Examples

			3^3-1 = 26 = 2*13, so a(3) = 2.
0 has no prime factors, so a(1) = 0.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A068601, A082863, A245909.

Programs

Maple

A240975 := proc(n)
    A001221(n^3-1) ;
end proc:

Mathematica

a[n_] := PrimeNu[n^3-1]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Sep 13 2024 *)

PARI

a(n) = if(n<=1,0,omega(n^3-1)); \\ Joerg Arndt, Aug 06 2014

Python

from sympy import primefactors
def A240975(n):
    return len(primefactors(n**3-1)) # Chai Wah Wu, Aug 06 2014

Formula

a(prime(n)) = A245909(n).

a(n) = A001221(A068601(n)) for n >= 2. - Michel Marcus, Aug 06 2014