A104484 Number of distinct prime divisors of 33...331 (with n 3s).

0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 2, 2, 3, 1, 3, 4, 3, 2, 4, 3, 3, 2, 4, 3, 3, 2, 3, 4, 6, 2, 2, 3, 3, 4, 4, 1, 3, 3, 6, 6, 3, 2, 3, 5, 3, 1, 3, 3, 4, 6, 3, 3, 5, 3, 5, 1, 3, 6, 5, 4, 3, 5, 3, 3, 5, 4, 6, 6, 3, 6, 2, 2, 4, 1, 5, 5, 5, 4, 4, 7, 2, 2, 5, 6

Offset: 0

Author

Parthasarathy Nambi, Apr 18 2005

Keywords

• nonn
• base

Comments

Interestingly, the first seven members in this sequence are all primes.

Examples

			Number of distinct prime divisors of 31 is 1 (prime).
Number of distinct prime divisors of 331 is 1 (prime).
Number of distinct prime divisors of 3331 is 1 (prime).
Number of distinct prime divisors of 33331 is 1 (prime).
Number of distinct prime divisors of 333331 is 1 (prime).
Number of distinct prime divisors of 3333331 is 1 (prime).
Number of distinct prime divisors of 33333331 is 1 (prime).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..203

Crossrefs

Cf. A001221, A033175, A051200, A105267.

Programs

Mathematica

Table[Length[FactorInteger[(10^(n + 1) - 7)/3]], {n, 1, 50}] (* Stefan Steinerberger *)

PARI

a(n) = omega((10^(n + 1) - 7)/3); \\ Michel Marcus, May 13 2020

Formula

a(n) = A001221(A033175(n+1)). - Amiram Eldar, Jan 24 2020, corrected, May 13 2020

Extensions

More terms from Amiram Eldar, Jan 24 2020

a(0) inserted by Amiram Eldar, May 13 2020