cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

This page as a plain text file.
%I A081395 #13 May 15 2023 08:46:40
%S A081395 1,6,13,25,72,96,182,320,481,923,1018,1321,1323,1670,3457,3455,3472,
%T A081395 3464,3462,3469,8222,9991,12163,15838,17665,18313,18480,19458,19464,
%U A081395 29708,36787,36796,36789,40048,43603,47210,47521,61653,61675,80722,87117,87120,92958,93181,93186,93187
%N 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.
%F A081395 a(n) = Min{k; A081389(k) = n}.
%e A081395 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.
%t A081395 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 *)
%Y A081395 Cf. A000108, A081389, A081393, A081394.
%K A081395 nonn
%O A081395 0,2
%A A081395 _Labos Elemer_, Mar 27 2003
%E A081395 a(11)-a(21) from _Michel Marcus_, Sep 01 2019
%E A081395 a(22)-a(45) from _Amiram Eldar_, May 15 2023