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

1,2

Comments

As in A034444, all terms are powers of 2.

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A001405, A034444, A034973.

Sequence in context: A279170 A292254 A292942 * A327649 A265529 A292597

Adjacent sequences: A039590 A039591 A039592 * A039594 A039595 A039596

Keyword

nonn

Author

Labos Elemer

Status

approved