A390328 Numbers k such that the number of prime divisors of binomial(2k, k), including multiplicities, is odd.

1, 3, 4, 5, 6, 12, 13, 14, 15, 16, 17, 18, 23, 24, 26, 30, 32, 35, 36, 39, 40, 41, 45, 50, 51, 53, 54, 55, 58, 60, 61, 63, 64, 66, 67, 68, 69, 75, 79, 80, 83, 84, 93, 95, 96, 98, 111, 114, 115, 117, 119, 128, 129, 130, 133, 137, 139, 140, 141, 142, 143, 145

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Example

Binomial(6,3) = 2^2*5, for a total of 3 prime divisors (where 2 has multiplicity 2), so 3 is in the list.

Mathematica

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

Crossrefs

Cf. A000984, A001222, A390327 (complement), A390329, A390330.

Sequence in context: A337177 A125139 A369762 * A107224 A026493 A177431

Adjacent sequences: A390325 A390326 A390327 * A390329 A390330 A390331

Keyword

nonn

Author

Clark Kimberling, Nov 01 2025

Status

approved