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.

1122, 1218, 5762, 11330, 12322, 15132, 16482, 26690, 37442, 40994, 57090, 61184, 77184, 94978, 103170, 107072, 108290, 114818, 121346, 124662, 136308, 138370, 142400, 148610, 149250, 149634, 177410, 198018, 221314, 221442, 233730, 246530, 259074, 264578

Offset: 1

Author

Vaclav Kotesovec, Sep 10 2019

Keywords

• nonn

Examples

			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).
		

Crossrefs

Cf. A080383, A327430, A080384, A080385, A080386, A080387.

Programs

Magma

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

Extensions

Terms > 100000 from Jon E. Schoenfield, Sep 15 2019