A080405 Number of distinct primes dividing n-th Catalan number.

0, 0, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 19, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 22, 22, 23, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25

Offset: 0

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

Examples

			a(5) = 3, as C(5) = 42 factors as 2*3*7 (3 distinct prime factors).
		

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A001221, A000108.

Cf. A081399.

Programs

Mathematica

PrimeNu[CatalanNumber[Range[0,80]]] (* Harvey P. Dale, Mar 27 2013 *)

PARI

C(n)=binomial(2*n,n)/(n+1);
for(n=1,100,print1(matsize(factor(C(n-1)))[1],", ")); \\ Joerg Arndt, Apr 19 2014

Formula

a(n) = A001221(A000108(n)).