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