A048244 a(n) = A048106(A001405(n)).

1, 2, 2, 4, 4, 2, 4, 8, 4, -2, 16, 8, 8, 0, 8, 16, 32, 16, 32, 16, 32, 0, 64, 32, -16, -64, -160, -256, -128, -224, 64, 128, 0, -256, 256, -128, -128, -512, 512, -256, 512, 0, 512, 0, -2048, -2816, -256, -1408, -1408, -2560, -2560, -4096, -1024, -1792, 2048

Offset

1,2

Comments

The terms indicate whether more, equal or fewer unitary than non-unitary divisors of the central binomial coefficient exists.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

a(n) = A034444(A001405(n)) - A048105(A001405(n)).

Example

For n = 54, binomial(54,27) has 3840 divisors of which 1024 are unitary and 2816 are not. The difference is -1792, so a(54) = -1792.

Mathematica

a[n_] := Module[{b = Binomial[n, Floor[n/2]]}, 2^(PrimeNu[b] + 1) - DivisorSigma[0, b]]; Array[a, 60] (* Amiram Eldar, Oct 05 2024 *)

Prog

(PARI) a048106(n) = (2^(1+omega(n)) - numdiv(n));
a(n) = a048106(binomial(n, n\2)); \\ Michel Marcus, May 14 2018

Crossrefs

Cf. A001405, A048106.

Sequence in context: A214516 A352502 A238004 * A056673 A353761 A128442

Adjacent sequences: A048241 A048242 A048243 * A048245 A048246 A048247

Keyword

sign

Author

Labos Elemer

Status

approved