A081388 Number of unitary prime divisors of the n-th Catalan number.

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

Offset: 1

Author

Labos Elemer, Mar 27 2003

Keywords

• nonn

Examples

			For n = 10: Catalan(10) = 16796 = 2^2*13*17*19, the unitary prime divisors are {13, 17, 19}, so a(10) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000108, A034444, A048105, A056169, A056170, A080405, A081386, A081387, A081389.

Programs

Mathematica

a[n_] := Count[FactorInteger[CatalanNumber[n]][[;;, 2]], 1]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Aug 16 2024 *)

PARI

nbupd(n) = my(f=factor(n)[, 2]); sum(i=1, #f, f[i]==1);
a(n) = nbupd(binomial(2*n, n)/(n+1)); \\ Michel Marcus, Sep 05 2017

Formula

a(n) = A056169(A000108(n)).