A390327 Numbers k such that the number of prime divisors of binomial(2k, k), including multiplicities, is even.

2, 7, 8, 9, 10, 11, 19, 20, 21, 22, 25, 27, 28, 29, 31, 33, 34, 37, 38, 42, 43, 44, 46, 47, 48, 49, 52, 56, 57, 59, 62, 65, 70, 71, 72, 73, 74, 76, 77, 78, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 94, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109

Offset

0,1

Links

Table of n, a(n) for n=0..62.

Example

Binomial(14,7) = (2^3)*3*11*13, for a total of 6 prime divisors (where 2 has multiplicity 3), so 7 is in the list.

Mathematica

u[n_] := PrimeOmega[Binomial[2 n, n]];
Select[Range[120], EvenQ[u[#]] &]

Crossrefs

Cf. A000984, A001222, A023816, A390328 (complement), A390329, A390330.

Sequence in context: A346309 A043054 A107225 * A253251 A093915 A152769

Adjacent sequences: A390324 A390325 A390326 * A390328 A390329 A390330

Keyword

nonn

Author

Clark Kimberling, Nov 01 2025

Status

approved