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A121943
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Numbers k such that the central binomial coefficient C(2k,k) is divisible by k^2.
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8
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1, 924, 1287, 2002, 2145, 3366, 3640, 3740, 4199, 6006, 6118, 6552, 7480, 7920, 8580, 8855, 10465, 10920, 11385, 11592, 12285, 12325, 12441, 12540, 12597, 12920, 13224, 13398, 13566, 15080, 15834, 18270, 18354, 18837, 18972, 19227, 23562, 23870, 25641, 25740
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by n^2. - Lucian Craciun, Feb 09 2017
The asymptotic density of this sequence is 0.00322778... (Ford and Konyagin, 2021). - Amiram Eldar, Jan 26 2021
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LINKS
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MATHEMATICA
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Select[Table[n, {n, 20000}], IntegerQ[Binomial[2#, # ]/#^2] &]
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PROG
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(Python)
from __future__ import division
for n in range(1, 10**5):
if not b % (n**2):
(PARI) lista(nn) = {for(n=1, nn, if(Mod(binomial(2*n, n), n^2) == 0, print1(n, ", "))); } \\ Altug Alkan, Mar 27 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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