A081390 Number k such that the k-th Catalan number has only one non-unitary prime divisor; all the other prime divisors have exponent one.

6, 10, 12, 15, 16, 20, 21, 22, 27, 28, 29, 30, 32, 33, 34, 36, 37, 39, 53, 54, 55, 56, 57, 58, 65, 67, 79, 80, 109, 110, 129, 135, 159, 161, 170, 171, 255, 783, 784, 785, 786, 902

Offset

1,1

Comments

a(43) > 25000, if it exists. - Amiram Eldar, Jul 22 2024

Links

Table of n, a(n) for n=1..42.

Example

902 is a term because binomial(1804,902)/903 has 189 prime factor, 188 stand with exponent one, but 2 with 5: 2^5.

Mathematica

c[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 1 &)]; Select[Range[0, 1000], c[CatalanNumber[#]] == 1 &] (* Amiram Eldar, Jul 22 2024 *)

Crossrefs

Cf. A000108, A081386, A081387, A081388, A081389, A080405, A080664.

Sequence in context: A108315 A134616 A362180 * A210578 A274426 A345995

Adjacent sequences: A081387 A081388 A081389 * A081391 A081392 A081393

Keyword

nonn,more

Author

Labos Elemer, Mar 27 2003

Status

approved