A080394 Numbers k such that binomial(k, floor(k/2)) is divisible by k^2.

1, 195, 273, 357, 385, 399, 585, 627, 665, 897, 935, 945, 957, 975, 1071, 1085, 1155, 1209, 1235, 1395, 1547, 1581, 1595, 1705, 1771, 1848, 1881, 1925, 1935, 1995, 2035, 2091, 2193, 2255, 2295, 2331, 2365, 2405, 2475, 2574, 2583, 2585, 2639, 2665, 2679

Offset: 1

Author

Labos Elemer, Mar 18 2003

Keywords

• nonn

Examples

			Very few values are even, like 1848 and 2574 (in A067348).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001405, A000984, A067348.

Cf. A073076.

Programs

Mathematica

Do[s=Binomial[n, Floor[n/2]]/n^2; If[IntegerQ[s], Print[n]], {n, 1, 10000}]

PARI

is(k) = !(binomial(k, k\2) % n^2); \\ Amiram Eldar, Aug 11 2024