A081395 a(n) is the smallest value of k such that number of non-unitary prime divisors of k-th Catalan number, A000108(k) = C(2*k,k)/(k+1) equals n.

1, 6, 13, 25, 72, 96, 182, 320, 481, 923, 1018, 1321, 1323, 1670, 3457, 3455, 3472, 3464, 3462, 3469, 8222, 9991, 12163, 15838, 17665, 18313, 18480, 19458, 19464, 29708, 36787, 36796, 36789, 40048, 43603, 47210, 47521, 61653, 61675, 80722, 87117, 87120, 92958, 93181, 93186, 93187

Offset: 0

Author

Labos Elemer, Mar 27 2003

Keywords

• nonn

Examples

			n=6: a(6)=182, C(364,182)/183 has 6 non-unitary prime divisors: {2,3,7,11,17,19} and 182 is the smallest.
		

Crossrefs

Cf. A000108, A081389, A081393, A081394.

Programs

Mathematica

seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 1, c = 0, i}, While[c < len && k < kmax, i = Count[FactorInteger[CatalanNumber[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 *)

Formula

a(n) = Min{k; A081389(k) = n}.

Extensions

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

a(22)-a(45) from Amiram Eldar, May 15 2023