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URL: https://oeis.org/A239624

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A239624
Conjecturally, the number of numbers k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).
2
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
0,1
COMMENTS
The 0th term is the largest number k such that binomial(2k,k) is squarefree.
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]]]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Mar 27 2014
STATUS
approved