A239623 Conjecturally, the largest k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).

4, 786, 785, 2080, 902, 2034, 2079, 1086, 2081, 2090, 1652, 2562, 3905, 8185, 4987, 3507, 5562, 2713, 3584, 4191, 8285, 9319, 12237, 12117, 12248, 9311, 8180, 8399, 9308, 20123, 11977, 11683, 12261, 14365, 15403, 20114, 16867, 19938, 19559, 20316, 24706

Offset

0,1

Comments

The last number in row n of A239622. The 0th term is the largest number k such that binomial(2k,k) is squarefree. The first 41 terms were checked by computing binomial(2k,k) for k <= 10^5. See the plot in A110493.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..125

Mathematica

b = 1; t = Table[b = b*(4 - 2/n); last = 0; Do[If[Mod[b, p^2] == 0, last = p], {p, Prime[Range[PrimePi[Sqrt[2*n]]]]}]; last, {n, 25000}]; t = Join[{0}, t]; Table[Flatten[Position[t, p]][[-1]] - 1, {p, Join[{0}, Prime[Range[20]]]}]

Crossrefs

Cf. A110493, A110494, A239622, A239624.

Sequence in context: A007725 A102195 A114766 * A202685 A172893 A072725

Adjacent sequences: A239620 A239621 A239622 * A239624 A239625 A239626

Keyword

nonn

Author

T. D. Noe, Mar 27 2014

Status

approved