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

Author

Labos Elemer, Mar 27 2003

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A081387, A081393, A081395, A056175.

Programs

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 *)

Formula

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

Extensions

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

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