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%I #26 Mar 05 2023 16:27:32
%S 5,7,9,11,15,17,19,21,23,27,29,33,35,39,43,45,47,49,51,53,55,59,61,63,
%T 65,67,69,71,73,75,77,79,81,83,87,89,93,95,97,99,101,103,105,107,109,
%U 111,113,115,117,119,121,123,125,127,129,131,135,137,139,141,143,145
%N Numbers k such that there are exactly 6 numbers j for which binomial(k, floor(k/2)) / binomial(k,j) is an integer, i.e., A080383(k) = 6.
%H Vaclav Kotesovec, <a href="/A080384/b080384.txt">Table of n, a(n) for n = 1..44084</a>
%e For n=9, the central binomial coefficient (C(9,4) = 126) is divisible by C(9,0), C(9,1), C(9,4), C(9,5), C(9,8), and C(9,9); certain primes are missing, certain composites are here.
%t Position[Table[Count[Binomial[n,Floor[n/2]]/Binomial[n,Range[0,n]],_?IntegerQ],{n,150}],6]//Flatten (* _Harvey P. Dale_, Mar 05 2023 *)
%o (PARI) isok(n) = my(b=binomial(n, n\2)); sum(i=0, n, (b % binomial(n, i)) == 0) == 6; \\ _Michel Marcus_, Jul 29 2017
%Y Cf. A327430, A080385, A080386, A327431, A080387.
%Y Cf. A001405, A057977.
%K nonn
%O 1,1
%A _Labos Elemer_, Mar 12 2003