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A327431 Numbers k such that there are exactly 9 numbers j for which binomial(k, floor(k/2)) / binomial(k,j) is an integer, i.e., A080383(k) = 9.

%I A327431 #15 Sep 20 2019 02:20:34
%S A327431 1122,1218,5762,11330,12322,15132,16482,26690,37442,40994,57090,61184,
%T A327431 77184,94978,103170,107072,108290,114818,121346,124662,136308,138370,
%U A327431 142400,148610,149250,149634,177410,198018,221314,221442,233730,246530,259074,264578
%N A327431 Numbers k such that there are exactly 9 numbers j for which binomial(k, floor(k/2)) / binomial(k,j) is an integer, i.e., A080383(k) = 9.
%e A327431 C(1122,561) is divisible by 9 binomial coefficients C(1122,0), C(1122,1), C(1122,2), C(1122,4), C(1122,561), C(1122,1118), C(1122,1120), C(1122,1121) and C(1122,1122).
%o A327431 (Magma)
%o A327431 a:=[]; kMax:=265000; cbc:=2; for k in [4..kMax by 2] do cbc:=(cbc*(4*k-4)) div k; count:=3; p:=PreviousPrime((k div 2) + 1); b:=1; for j in [1..k-2*p] do b:=(b*(k+1-j)) div j; if cbc mod b eq 0 then count+:=2; end if; end for; r:=1/1; for j in [(k div 2)-1..p by -1] do r:=r*(j+1)/(k-j); end for; if r le 1/2 then b:=cbc; for j in [(k div 2)-1..p by -1] do b:=(b*(j+1)) div (k-j); if cbc mod b eq 0 then count+:=2; end if; end for; end if; if count eq 9 then a[#a+1]:=k; end if; end for; a // _Jon E. Schoenfield_, Sep 15 2019
%Y A327431 Cf. A080383, A327430, A080384, A080385, A080386, A080387.
%K A327431 nonn
%O A327431 1,1
%A A327431 _Vaclav Kotesovec_, Sep 10 2019
%E A327431 Terms > 100000 from _Jon E. Schoenfield_, Sep 15 2019