A080394 - OEIS

%I #11 Aug 11 2024 04:58:22

%S 1,195,273,357,385,399,585,627,665,897,935,945,957,975,1071,1085,1155,

%T 1209,1235,1395,1547,1581,1595,1705,1771,1848,1881,1925,1935,1995,

%U 2035,2091,2193,2255,2295,2331,2365,2405,2475,2574,2583,2585,2639,2665,2679

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

%H Amiram Eldar, <a href="/A080394/b080394.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (PARI) is(k) = !(binomial(k, k\2) % n^2); \\ _Amiram Eldar_, Aug 11 2024

%Y Cf. A001405, A000984, A067348.

%Y Cf. A073076.

%K nonn

%O 1,2

%A _Labos Elemer_, Mar 18 2003