A048195 Numbers k for which binomial(k, floor(k/2)) has fewer unitary than non-unitary divisors.

10, 25, 26, 27, 28, 29, 30, 34, 36, 37, 38, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 60, 61, 62, 63, 64, 66, 68, 69, 70, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 110

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

A048111 applied to central binomial coefficients.

Examples

			k = 58: binomial(58,29) has 20480 divisors, 8192 unitary ones and 12288 non-unitary ones, and 8192 < 12288.
		

Links

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

Crossrefs

Cf. A001405, A034444, A048105, A048111.

Programs

Mathematica

q[n_] := Module[{e = FactorInteger[Binomial[n, Floor[n/2]]][[;; , 2]]}, Times @@ (e + 1) > 2^(Length[e] + 1)]; Select[Range[120], q] (* Amiram Eldar, Oct 05 2024 *)

PARI

nbud(n) = 1<A034444
isok(n) = my(b=binomial(n, n\2)); numdiv(b) > 2*nbud(b); \\ Michel Marcus, Mar 15 2018

Formula

A034444(A001405(k)) < A048105(A001405(k)).

Extensions

More terms from Michel Marcus, Mar 15 2018