A080384 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.

5, 7, 9, 11, 15, 17, 19, 21, 23, 27, 29, 33, 35, 39, 43, 45, 47, 49, 51, 53, 55, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 87, 89, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 135, 137, 139, 141, 143, 145

Offset: 1

Author

Labos Elemer, Mar 12 2003

Keywords

• nonn

Examples

			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.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..44084

Crossrefs

Cf. A327430, A080385, A080386, A327431, A080387.

Cf. A001405, A057977.

Programs

Mathematica

Position[Table[Count[Binomial[n,Floor[n/2]]/Binomial[n,Range[0,n]],?IntegerQ],{n,150}],6]//Flatten (* _Harvey P. Dale, Mar 05 2023 *)

PARI

isok(n) = my(b=binomial(n, n\2)); sum(i=0, n, (b % binomial(n, i)) == 0) == 6; \\ Michel Marcus, Jul 29 2017