A105561 a(n) is the m-th prime, where m is the number of distinct prime factors of n (A001221), a(1) = 1.

1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 5, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 5, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 5, 2, 3, 3, 2, 3, 5, 2, 3, 3, 5, 2, 3, 2, 3, 3, 3, 3, 5, 2, 3, 2, 3, 2, 5, 3, 3, 3, 3, 2, 5, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 5, 2, 3, 5, 3, 2, 3, 2, 5, 3, 3, 2, 5, 3, 3, 3, 3, 3, 5

Offset: 1

Author

Cino Hilliard, May 03 2005

Keywords

• easy
• nonn

Comments

Term a(1) = 1 prepended to match with the definition of A105560. - Antti Karttunen, May 25 2017

Examples

			Let n = 6; 6 has 2 different prime factors, therefore a(6) = 3, the second prime.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001221, A105555, A105560.

Programs

Mathematica

Table[Prime[Length[FactorInteger[n]]], {n, 2, 84}]
Prime[PrimeNu[Range[2,90]]] (* Harvey P. Dale, Oct 02 2013 *)

PARI

A105561(n) = if(1==n,n,prime(omega(n))); \\ [After the original Pari-program given here.] - Antti Karttunen, May 25 2017

Python

from sympy import prime, primefactors
def a(n): return 1 if n==1 else prime(len(primefactors(n))) # Indranil Ghosh, May 25 2017

Extensions

Edited by Stefan Steinerberger, Jun 15 2007

Term a(1) = 1 prepended (correcting also the indexing of the rest of terms), and data section extended to 120 terms by Antti Karttunen, May 25 2017