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A081388 Number of unitary prime divisors of the n-th Catalan number. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A143998 A054237 A129600 * A231070 A230252 A295424

Adjacent sequences:  A081385 A081386 A081387 * A081389 A081390 A081391

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 27 2003

STATUS

approved

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Last modified September 20 06:51 EDT 2020. Contains 337264 sequences. (Running on oeis4.)