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.

A081393 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A000984(k) = C(2*k,k) equals n.

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%I A081393 #14 May 15 2023 08:46:44
%S A081393 1,3,5,14,48,74,182,314,480,774,960,1321,1323,1670,3121,3455,3457,
%T A081393 3472,3462,3469,8203,9991,12163,15838,15840,17665,18480,18482,19458,
%U A081393 19464,36782,19865,36789,40048,43603,43655,47518,61654,61653,61685,61684,87120,92958,93181,93185,93187,93191
%N A081393 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A000984(k) = C(2*k,k) equals n.
%F A081393 a(n) = Min{k; A081387(k) = n}.
%e A081393 n=5: a(5)=74, C(148,74) has 5 non-unitary prime divisors: {2,3,5,7,11} and 74 is the smallest.
%t A081393 seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 1, c = 0, i}, While[c < len && k < kmax, i = Count[FactorInteger[Binomial[2*k, 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 A081393 Cf. A081387, A081394, A081395.
%K A081393 nonn
%O A081393 0,2
%A A081393 _Labos Elemer_, Mar 27 2003
%E A081393 a(11)-a(21) from _Michel Marcus_, Sep 01 2019
%E A081393 a(22)-a(46) from _Amiram Eldar_, May 15 2023