A389396 Numbers k such that binomial(2*k,k) is divisible by (k+1)^2*(k+2)^2.

208, 458, 987, 1220, 1455, 1597, 1889, 2012, 2144, 2330, 2477, 2663, 2991, 3353, 3415, 3430, 3439, 3475, 3476, 3551, 3563, 3568, 3617, 3625, 3722, 4087, 4093, 4344, 5528, 5642, 5794, 6098, 6160, 6312, 6439, 6488, 7083, 7105, 7118, 7666, 7703, 8174, 8175, 8176

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1468 (terms 1..913 from Stijn Cambie)

Thomas Bloom, Problem 727, Erdős Problems.

Prog

(SageMath) def isok(n): return (binomial(2*n, n)%(n+2)**2==0 and binomial(2*n, n)%(n+1)**2==0)
[n for n in range(1, 10000) if isok(n)]
(PARI) isok(k) = !(binomial(2*k, k) % ((k+1)^2*(k+2)^2)); \\ Michel Marcus, Oct 09 2025

Crossrefs

Cf. A002503, A065350, A065344, A065345, A065346, A065347, A065348, A065349.

Sequence in context: A260365 A131686 A235273 * A255082 A255075 A304281

Adjacent sequences: A389393 A389394 A389395 * A389397 A389398 A389399

Keyword

nonn,easy

Author

Stijn Cambie, Oct 02 2025

Status

approved