A081391 Numbers k such that the central binomial coefficient C(2*k,k) has only one prime divisor whose exponent equals one.

3, 6, 7, 8, 9, 10, 11, 12, 16, 21, 22, 28, 29, 30, 31, 36, 37, 54, 55, 57, 58, 110, 171, 784, 786

Offset: 1

Author

Labos Elemer, Mar 27 2003

Keywords

• nonn
• more

Comments

Numbers k such that C(2*k,k) has one non-unitary prime divisor.

Numbers k for which A081387(k) = 1.

No more terms through 10^6; conjecture: no terms after 786. - Jon E. Schoenfield, Jul 29 2017

Examples

			For k = 786, C(1572,786) = 2*2*2*2*m, where m is a squarefree product of 169 primes.
		

Crossrefs

Cf. A000108, A000984, A001405, A046098, A081386, A081387, A081388, A081389, A081390, A080664.

Programs

Mathematica

q[k_] := Count[FactorInteger[Binomial[2*k, k]][[;;, 2]], ?( # > 1 &)] == 1; Select[Range[1000], q] (* _Amiram Eldar, Oct 05 2024 *)

PARI

is(k) = {my(e = factor(binomial(2*k, k))[, 2]); sum(i = 1, #e, e[i] > 1) == 1;} \\ Amiram Eldar, Oct 05 2024