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

0,9

Comments

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

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A001221, A033175, A051200, A105267.

Sequence in context: A132328 A064822 A238337 * A038809 A337496 A078342

Adjacent sequences: A104481 A104482 A104483 * A104485 A104486 A104487

Keyword

nonn,base

Author

Parthasarathy Nambi, Apr 18 2005

Extensions

More terms from Amiram Eldar, Jan 24 2020

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

Status

approved