login
A081391
Numbers k such that the central binomial coefficient C(2*k,k) has only one prime divisor whose exponent equals one.
2
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
1,1
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
EXAMPLE
For k = 786, C(1572,786) = 2*2*2*2*m, where m is a squarefree product of 169 primes.
MATHEMATICA
q[k_] := Count[FactorInteger[Binomial[2*k, k]][[;; , 2]], _?( # > 1 &)] == 1; Select[Range[1000], q] (* Amiram Eldar, Oct 05 2024 *)
PROG
(PARI) is(k) = {my(e = factor(binomial(2*k, k))[, 2]); sum(i = 1, #e, e[i] > 1) == 1; } \\ Amiram Eldar, Oct 05 2024
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Mar 27 2003
STATUS
approved