A080405 - OEIS

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A080405

Number of distinct primes dividing n-th Catalan number.

5

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

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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.

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