A116505 Number of distinct prime divisors of the concatenation of 1..n.

0, 2, 2, 2, 3, 3, 2, 4, 3, 3, 6, 4, 3, 3, 3, 3, 4, 5, 6, 6, 8, 6, 4, 5, 4, 6, 5, 5, 4, 7, 3, 5, 6, 2, 7, 5, 4, 4, 6, 8, 5, 7, 4, 4, 9, 7, 5, 7, 6, 9, 3, 3, 4, 9, 5, 4, 6, 4, 4, 6, 3, 7, 4, 9, 6, 8, 3, 7, 7, 6, 5, 5, 3, 9, 5, 4, 5, 6, 6, 7, 4, 7, 6, 3, 5, 7, 6, 5, 9, 8, 6, 6, 7, 5, 6, 5, 2, 9, 5, 9

Offset: 1

Author

Parthasarathy Nambi, Mar 20 2006

Keywords

• nonn
• base

Comments

Dario Alpern's factorization program was used for n > 43.

Examples

			123456 = 2*2*2*2*2*2*3*643, with distinct prime divisors 2, 3 and 643. Hence, a(6) = 3.
		

Links

• Dario Alpern, Factorization using the Elliptic Curve Method

Crossrefs

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793.

Programs

Mathematica

Table[PrimeNu[FromDigits[Flatten[IntegerDigits[Range[n]]]]], {n, 30}] (* Jan Mangaldan, Jul 07 2020 *)

PARI

{a="";for(n=1,43,a=concat(a,n);print1(omega(eval(a)),", "))}

Extensions

Edited and extended by Klaus Brockhaus, Mar 29 2006

Terms 59-100 from Sean A. Irvine, Nov 04 2009