A081394 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A001405(k) = C(k, floor(k/2)) equals n.

1, 6, 10, 27, 96, 147, 363, 627, 959, 1547, 1919, 2641, 2645, 3339, 6241, 6909, 6913, 6943, 6923, 6937, 16405, 19981, 24325, 31675, 31679, 35329, 36959, 36963, 38915, 38927, 73563, 39729, 73577, 80095, 87205, 87309, 95035, 123307, 123305, 123369, 123367, 174239, 185915, 186361, 186369, 186373, 186381

Offset

0,2

Links

Table of n, a(n) for n=0..46.

Formula

a(n) = Min{k; A056175(k) = n}.

Example

n=8: a(8)=959, C(959,479) has 8 non-unitary prime divisors: {2,3,5,7,11,13,23,29} and 959 is the smallest.

Mathematica

seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 1, c = 0, i}, While[c < len && k < kmax, i = Count[FactorInteger[Binomial[k, Floor[k/2]]][[;; , 2]], _?(# > 1 &)] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = k]; k++]; TakeWhile[s, # > 0 &]]; seq[20, 10^4] (* Amiram Eldar, May 15 2023 *)

Crossrefs

Cf. A081387, A081393, A081395, A056175.

Sequence in context: A324617 A359145 A287989 * A184387 A295185 A225845

Adjacent sequences: A081391 A081392 A081393 * A081395 A081396 A081397

Keyword

nonn

Author

Labos Elemer, Mar 27 2003

Extensions

a(9)-a(19) from Michel Marcus, Sep 01 2019

a(20)-a(46) from Amiram Eldar, May 15 2023

Status

approved