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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 15:57 EDT 2024. Contains 375853 sequences. (Running on oeis4.)