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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..51.

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

Cf. A110493, A110494, A239622, A239623.

Sequence in context: A030716 A169599 A106684 * A179628 A339392 A030653

Adjacent sequences:  A239621 A239622 A239623 * A239625 A239626 A239627

KEYWORD

nonn

AUTHOR

T. D. Noe, Mar 27 2014

STATUS

approved

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Last modified May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)