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

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

Author

T. D. Noe, Mar 27 2014

Keywords

• nonn

Comments

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

Crossrefs

Cf. A110493, A110494, A239622, A239623.

Programs

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