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

1,4

Links

Table of n, a(n) for n=1..78.

Formula

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

Example

n = 10: Catalan(20) = 16796 = 2*2*13*17*19, unitary p-divisors = {13,17,19}, so a(20) = 3.

Prog

(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

Crossrefs

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

Sequence in context: A360495 A129600 A355663 * A231070 A230252 A295424

Adjacent sequences: A081385 A081386 A081387 * A081389 A081390 A081391

Keyword

nonn

Author

Labos Elemer, Mar 27 2003

Status

approved