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Numbers k such that binomial(k, floor(k/2)) is not divisible by k.
4

%I #10 Aug 24 2024 06:06:03

%S 4,6,8,10,14,16,18,20,22,24,26,28,32,34,36,38,40,42,44,46,48,50,52,54,

%T 58,60,62,64,66,68,70,72,74,76,78,80,82,86,88,92,94,96,98,100,102,104,

%U 106,108,110,112,114,116,118,120,122,124,126,128,130,134,136,138,140

%N Numbers k such that binomial(k, floor(k/2)) is not divisible by k.

%C All the terms are even. - _Amiram Eldar_, Aug 24 2024

%H Amiram Eldar, <a href="/A067315/b067315.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[ Range[ 2, 150, 2 ], Mod[ Binomial[ #, #/2 ], # ]>0& ]

%o (PARI) is(k) = binomial(k, k\2) % k > 0; \\ _Amiram Eldar_, Aug 24 2024

%Y Cf. A001405, A042970, A042996 (complement), A067348.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 14 2002