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

0,2

Links

Table of n, a(n) for n=0..45.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000108, A081389, A081393, A081394.

Sequence in context: A101736 A162432 A117072 * A343007 A192762 A268721

Adjacent sequences: A081392 A081393 A081394 * A081396 A081397 A081398

Keyword

nonn

Author

Labos Elemer, Mar 27 2003

Extensions

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

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

Status

approved