A080395 Even numbers k such that the central binomial coefficient A000984(k, k/2) is divisible by k^2.

1848, 2574, 4004, 4290, 6732, 7480, 8398, 12012, 12236, 17710, 20930, 22770, 24570, 24650, 24882, 25080, 25194, 26796, 27132, 30160, 31668, 36540, 36708, 37674, 37944, 38454, 47124, 47740, 51282, 51480, 53200, 57288, 62160, 68376, 69930, 70840, 73260, 75480, 83640

Offset: 1

Author

Labos Elemer, Mar 18 2003

Keywords

• nonn

Comments

a(n)/2 is a term of A121943 for all n. - Amiram Eldar, Mar 07 2022

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001405, A000984, A067348, A080394, A121943.

Programs

Mathematica

Do[s=Binomial[n, n/2]/n^2; If[IntegerQ[s], Print[n]], {n, 1, 50000}]
Select[2Range[50000],Mod[Binomial[#,#/2],#^2]==0&] (* Harvey P. Dale, Jan 27 2025 *)

Extensions

Name corrected and more terms added by Amiram Eldar, Mar 07 2022