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A081388
Number of unitary prime divisors of the n-th Catalan number.
5
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
FORMULA
a(n) = A056169(A000108(n)).
EXAMPLE
For n = 10: Catalan(10) = 16796 = 2^2*13*17*19, the unitary prime divisors are {13, 17, 19}, so a(10) = 3.
MATHEMATICA
a[n_] := Count[FactorInteger[CatalanNumber[n]][[;; , 2]], 1]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Aug 16 2024 *)
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 27 2003
STATUS
approved