A081394 - OEIS

%I #13 May 15 2023 08:46:37

%S 1,6,10,27,96,147,363,627,959,1547,1919,2641,2645,3339,6241,6909,6913,

%T 6943,6923,6937,16405,19981,24325,31675,31679,35329,36959,36963,38915,

%U 38927,73563,39729,73577,80095,87205,87309,95035,123307,123305,123369,123367,174239,185915,186361,186369,186373,186381

%N 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.

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

%e 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.

%t 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 *)

%Y Cf. A081387, A081393, A081395, A056175.

%K nonn

%O 0,2

%A _Labos Elemer_, Mar 27 2003

%E a(9)-a(19) from _Michel Marcus_, Sep 01 2019

%E a(20)-a(46) from _Amiram Eldar_, May 15 2023