Checked all k < 10^8. a(1) has been proved. a(2) and a(3) are conjectured.
Checked all k < 10^9. a(4) is at least 537927682. - T. D. Noe, Jul 27 2005
Table of n, a(n) for n=1..3.
a(1)=4 because binomial(8,4) is the largest squarefree central binomial coefficient. a(2)=1056 because binomial(2112,1056) is the largest cubefree.
Cf. A110495 (n such that binomial(2n, n) is cubefree).
Sequence in context: A004804 A221228 A159859 * A009013 A248656 A221383
Adjacent sequences: A110496 A110497 A110498 * A110500 A110501 A110502
T. D. Noe, Jul 22 2005