A239622 -id:A239622 - cp's OEIS frontend

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

T. D. Noe, Mar 27 2014

nonn

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.

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

Cf. A110493, A110494, A239622, A239624.

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]]]}]

A239624 Conjecturally, the number of numbers k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).

Original entry on oeis.org

4, 23, 38, 50, 51, 54, 65, 70, 107, 127, 127, 165, 155, 150, 239, 287, 280, 179, 336, 314, 230, 453, 423, 600, 612, 419, 246, 454, 455, 892, 1117, 624, 916, 432, 1115, 363, 934, 1061, 763, 1073, 1203, 524, 1523, 559, 1278, 735, 2221, 1987, 929, 475, 1179, 1605

Offset: 0

T. D. Noe, Mar 27 2014

nonn

The 0th term is the largest number k such that binomial(2k,k) is squarefree.

Cf. A110493, A110494, A239622, A239623.

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, 20000}]; t = Join[{0}, t]; Table[Length[Position[t, p]], {p, Join[{0}, Prime[Range[20]]]}]

cp's OEIS Frontend

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

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