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

Author

Labos Elemer, Mar 27 2003

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

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

Programs

Mathematica

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