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.

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

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; unitary-p-divisors = {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, A081387-A081389, A034444, A048105, A056170, A056169.

Sequence in context: A100714 A339364 A050123 * A213712 A143802 A177040

Adjacent sequences: A081383 A081384 A081385 * A081387 A081388 A081389

Keyword

nonn

Author

Labos Elemer, Mar 27 2003

Status

approved