A119704 a(n) = number of distinct prime factors of 10^n+1 = omega(10^n+1).

1, 1, 1, 3, 2, 2, 2, 2, 2, 5, 3, 4, 3, 3, 4, 7, 5, 4, 3, 2, 4, 7, 4, 5, 3, 5, 3, 7, 4, 3, 7, 2, 4, 8, 4, 5, 6, 4, 3, 9, 4, 3, 7, 4, 4, 12, 4, 4, 9, 4, 7, 8, 4, 2, 6, 9, 5, 6, 5, 4, 6, 3, 3, 11, 3, 6, 8, 2, 4, 10, 11, 3, 5, 4, 7, 11, 6, 11, 7, 4, 9, 11, 3, 7, 8, 8, 3, 8, 4, 4, 11, 6, 4, 8, 4, 6, 8, 4

Offset: 0

Author

Lekraj Beedassy, Jun 09 2006

Keywords

• nonn

Examples

			a(1) = number of distinct prime factors of 11 = 1.
a(3) = number of distinct prime factors of 1001 = 3.
a(11) = 4 because 10^11+1 = 11*11*23*4093*8779 has 4 distinct factors.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..331 [First 309 terms from Ray Chandler, from the Kamada link]
• Makoto Kamada, Factorizations of 100...001.

Crossrefs

Cf. A001221, A003021, A038371, A057934, A062397.

Programs

Mathematica

Table[Length[FactorInteger[10^n + 1]], {n, 0, 50}] (* Stefan Steinerberger, Jun 13 2006 *)
PrimeNu[10^Range[0,100]+1] (* The program will take some time to run *) (* Harvey P. Dale, Aug 27 2019 *)

Formula

a(n) = A001221(A062397(n)). - Ray Chandler, May 02 2017

Extensions

More terms from Don Reble, Jun 13 2006