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

0,5

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001221, A000108.

Cf. A081399.

Sequence in context: A121536 A285761 A348385 * A039728 A332965 A354779

Adjacent sequences: A080402 A080403 A080404 * A080406 A080407 A080408

Keyword

nonn

Author

Labos Elemer, Mar 19 2003

Status

approved