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

1,1

Comments

A048111 applied to central binomial coefficients.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001405, A034444, A048105, A048111.

Sequence in context: A225974 A251317 A251201 * A133634 A174051 A274046

Adjacent sequences: A048192 A048193 A048194 * A048196 A048197 A048198

Keyword

nonn

Author

Labos Elemer

Extensions

More terms from Michel Marcus, Mar 15 2018

Status

approved