%I #19 May 13 2020 07:04:07
%S 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,
%T 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,
%U 5,4,6,6,3,6,2,2,4,1,5,5,5,4,4,7,2,2,5,6
%N Number of distinct prime divisors of 33...331 (with n 3s).
%C Interestingly, the first seven members in this sequence are all primes.
%H Amiram Eldar, <a href="/A104484/b104484.txt">Table of n, a(n) for n = 0..203</a>
%F a(n) = A001221(A033175(n+1)). - _Amiram Eldar_, Jan 24 2020, corrected, May 13 2020
%e Number of distinct prime divisors of 31 is 1 (prime).
%e Number of distinct prime divisors of 331 is 1 (prime).
%e Number of distinct prime divisors of 3331 is 1 (prime).
%e Number of distinct prime divisors of 33331 is 1 (prime).
%e Number of distinct prime divisors of 333331 is 1 (prime).
%e Number of distinct prime divisors of 3333331 is 1 (prime).
%e Number of distinct prime divisors of 33333331 is 1 (prime).
%t Table[Length[FactorInteger[(10^(n + 1) - 7)/3]], {n, 1, 50}] (* _Stefan Steinerberger_ *)
%o (PARI) a(n) = omega((10^(n + 1) - 7)/3); \\ _Michel Marcus_, May 13 2020
%Y Cf. A001221, A033175, A051200, A105267.
%K nonn,base
%O 0,9
%A _Parthasarathy Nambi_, Apr 18 2005
%E More terms from _Amiram Eldar_, Jan 24 2020
%E a(0) inserted by _Amiram Eldar_, May 13 2020