A039593 Number of unitary divisors of central binomial coefficients.

1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 16, 16, 16, 16, 16, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 256, 256, 256, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 4096, 4096

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

As in A034444, all terms are powers of 2.

Examples

			At n=5, the central binomial coefficient is 10, having 4 divisors, each of which is unitary, so a(5)=4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001405, A034444, A034973.

Programs

Mathematica

a[n_] := 2^PrimeNu[Binomial[n, Floor[n/2]]]; Array[a, 56] (* Amiram Eldar, Oct 06 2019 *)

Formula

a(n) = A034444(A001405(n)) = 2^A034973(n).