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.
%I A282163 #56 Jan 10 2022 05:27:04
%S A282163 1,154836,985320,1108536,1113959,1492260,1576696,1632708,1649238,
%T A282163 1684540,1805570,1988008,2508792,2548810,2550408,2659260,2698740,
%U A282163 2746590,2995122,3074552,3286710,3330795,3538458,3574200,3730155,4039932,4160240,4318548,4374370,4426695,4523985
%N A282163 Numbers k such that the central binomial coefficient C(2*k,k) is divisible by k^3.
%C A282163 Equivalently, numbers k such that the k-th Catalan number C(2*k,k)/(k+1) is divisible by k^3. - _Lucian Craciun_, Feb 09 2017
%C A282163 The asymptotic density of this sequence is 0.000031511777... (Ford and Konyagin, 2021). - _Amiram Eldar_, Jan 26 2021
%H A282163 Lucian Craciun, <a href="/A282163/b282163.txt">Table of n, a(n) for n = 1..16000</a> (corrected and extended by Giovanni Resta)
%H A282163 Kevin Ford and Sergei Konyagin, <a href="https://doi.org/10.1090/tran/8183">Divisibility of the central binomial coefficient binomial(2n, n)</a>, Trans. Amer. Math. Soc., Vol. 374, No. 2 (2021), pp. 923-953; <a href="https://arxiv.org/abs/1909.03903">arXiv preprint</a>, arXiv:1909.03903 [math.NT], 2019-2020.
%H A282163 Wikipedia Mathematics Reference Desk, <a href="http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2017_February_9#n4_divides_Central_binomial_coefficient">n^4 Divides Central Binomial Coefficient</a>.
%e A282163 The central binomial coefficient C(2*154836,154836) is divisible by 154836^3.
%p A282163 A282163 := proc (n, m) local a, cbc, k; a := {}; cbc := binomial(2*n, n); for k from n+1 to m do cbc := cbc*(4-2/k); if type(cbc/k^3, integer) then a := `union`(a, {k}) end if end do; a end proc; A282163(0, 10^6)
%t A282163 Select[Table[n, {n, 10^6}], IntegerQ[Binomial[2#, #]/#^3] &] (* for small n *)
%t A282163 n := 0; m := 10^6; A282163 := {}; cbc := Binomial[2n, n]; For[k := n+1, k <= m, k++, {cbc *= 4-2/k, If[IntegerQ[cbc/k^3], A282163 = Append[A282163, k]]}] (* for large m *)
%t A282163 A282163:={}; k:=3; For[n:=1, n<=10^6, n++, {f=FactorInteger[n], For[j:=1, j<=Length[f], j++, {b=True, If[Sum[Floor[2n/f[[j, 1]]^i]-2 Floor[n/f[[j, 1]]^i], {i, 1, Length[IntegerDigits[2n, f[[j, 1]]]]}]<f[[j, 2]]k, {b=False, Break[]}]}], If[b, A282163=Append[A282163, n]]}] (* Legendre's formula for drastic time reduction, _Lucian Craciun_, Feb 28 2017; optimized by _Lucian Craciun_, Mar 02 2017 *)
%Y A282163 Cf. A000108, A000984, A014847, A121943, A282346, A283073, A283074, A282672.
%K A282163 nonn
%O A282163 1,2
%A A282163 _Lucian Craciun_, Feb 07 2017