A081393 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A000984(k) = C(2*k,k) equals n.

1, 3, 5, 14, 48, 74, 182, 314, 480, 774, 960, 1321, 1323, 1670, 3121, 3455, 3457, 3472, 3462, 3469, 8203, 9991, 12163, 15838, 15840, 17665, 18480, 18482, 19458, 19464, 36782, 19865, 36789, 40048, 43603, 43655, 47518, 61654, 61653, 61685, 61684, 87120, 92958, 93181, 93185, 93187, 93191

Offset

0,2

Links

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

Formula

a(n) = Min{k; A081387(k) = n}.

Example

n=5: a(5)=74, C(148,74) has 5 non-unitary prime divisors: {2,3,5,7,11} and 74 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[2*k, k]][[;; , 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, A081394, A081395.

Sequence in context: A230585 A006395 A078718 * A338368 A129326 A167553

Adjacent sequences: A081390 A081391 A081392 * A081394 A081395 A081396

Keyword

nonn

Author

Labos Elemer, Mar 27 2003

Extensions

a(11)-a(21) from Michel Marcus, Sep 01 2019

a(22)-a(46) from Amiram Eldar, May 15 2023

Status

approved