A245909 The number of distinct prime factors of prime(n)^3-1.

1, 2, 2, 3, 4, 3, 2, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 5, 5, 4, 3, 5, 4, 3, 3, 3, 4, 5, 4, 4, 4, 4, 5, 5, 5, 5, 4, 5, 3, 3, 4, 5, 6, 4, 4, 4, 7, 4, 4, 5, 4, 5, 4, 4, 3, 5, 5, 4, 6, 5, 5, 3, 5, 5, 4, 4, 6, 5, 5, 5, 4, 5, 5, 6, 5, 3, 4, 5, 4, 4, 5, 5, 6, 4, 5, 5, 4

Offset: 1

Author

R. J. Mathar, Aug 05 2014

Keywords

• nonn

Links

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

Programs

Magma

[#PrimeDivisors(p^3-1): p in PrimesUpTo(500)]; // Bruno Berselli, Aug 06 2014

Maple

A245909 := proc(n)
    A001221(ithprime(n)^3-1) ;
end proc:

Mathematica

Table[PrimeNu[Prime[n]^3 - 1], {n, 100}] (* Vincenzo Librandi, Aug 06 2014 *)

PARI

vector(500, n, omega(prime(n)^3-1)) \\ Derek Orr, Aug 05 2014

Python

from sympy import primefactors,prime
def A245909(n):
    return len(primefactors(prime(n)**3-1)) # Chai Wah Wu, Aug 05 2014

Formula

a(n) = A001221(A030078(n)-1).