

A081386


Number of unitary prime divisors of central binomial coefficient, C(2n,n) = A000984(n), i.e., number of those prime factors in C(2n,n), whose exponent equals one.


8



1, 2, 1, 3, 1, 3, 3, 4, 4, 4, 5, 5, 4, 3, 5, 7, 6, 7, 7, 8, 9, 9, 6, 7, 7, 7, 8, 11, 12, 11, 11, 11, 12, 12, 12, 13, 13, 13, 11, 13, 12, 14, 13, 13, 15, 14, 14, 14, 15, 16, 16, 16, 17, 19, 18, 17, 18, 19, 18, 19, 18, 18, 18, 20, 18, 21, 22, 20, 20, 20, 20, 20, 20, 19, 21, 21, 24, 23
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OFFSET

1,2


LINKS

T. D. Noe, Table of n, a(n) for n=1..2000


FORMULA

a(n) = A056169(A000984(n)).


EXAMPLE

n=10: C(20,10) = 184756 = 2*2*11*13*17*19; unitarypdivisors = {11,13,17,19}, so a(10)=4.


MATHEMATICA

Table[Function[m, Count[Divisors@ m, k_ /; And[PrimeQ@ k, GCD[k, m/k] == 1]]]@ Binomial[2 n, n], {n, 50}] (* Michael De Vlieger, Dec 17 2016 *)


PROG

(PARI) a(n) = my(f=factor(binomial(2*n, n))); sum(k=1, #f~, f[k, 2] == 1); \\ Michel Marcus, Dec 18 2016


CROSSREFS

Cf. A000984, A067434, A081387A081389, A034444, A048105, A056170, A056169.
Sequence in context: A111248 A100714 A050123 * A213712 A143802 A177040
Adjacent sequences: A081383 A081384 A081385 * A081387 A081388 A081389


KEYWORD

nonn


AUTHOR

Labos Elemer, Mar 27 2003


STATUS

approved



