A265401 Numbers n for which gcd{k=1..n-1} binomial(2*n, 2*k) = 1.

20, 26, 33, 35, 38, 39, 44, 46, 48, 50, 56, 58, 60, 62, 68, 72, 74, 77, 78, 80, 86, 88, 92, 93, 94, 95, 98, 102, 104, 105, 108, 110, 111, 116, 118, 119, 124, 130, 133, 134, 138, 140, 143, 144, 146, 148, 150, 152, 155, 158, 160, 161, 164, 165, 168, 170, 171, 176, 178, 182, 183, 185, 186, 188, 189, 194, 198, 200

Offset: 1

Author

Antti Karttunen, Dec 08 2015

Keywords

• nonn

Comments

Contains no primes or prime powers. - Robert Israel, Dec 10 2015

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6571

Crossrefs

Cf. A265388.

Programs

Maple

select(n -> igcd(seq(binomial(2*n, 2*k), k=1..n-1)) = 1, [$1..200]); # Robert Israel, Dec 10 2015

Mathematica

Select[Range@ 200, GCD @@ Table[Binomial[2 #, 2 k], {k, # - 1}] == 1 &] (* Michael De Vlieger, Dec 09 2015, modified to match the new corrected definition by Antti Karttunen, Dec 11 2015 *)

PARI

isok(n) = (n>1) && gcd(vector(n-1, k, binomial(2*n, 2*k))) == 1; \\ Michel Marcus, Dec 08 2015, edited by Antti Karttunen, Dec 11 2015 (see A265388 for why).