A390330 Numbers k such that the number of distinct prime divisors of binomial(2k, k) is odd.

1, 4, 5, 8, 9, 10, 15, 18, 19, 23, 29, 32, 38, 40, 41, 45, 46, 47, 53, 55, 56, 57, 60, 61, 62, 63, 66, 68, 69, 70, 71, 75, 76, 80, 81, 82, 83, 84, 85, 91, 93, 94, 95, 98, 100, 101, 104, 105, 106, 107, 108, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

Offset

0,2

Links

Table of n, a(n) for n=0..60.

Example

Binomial(10,5) = (2^2)*(3^2)*7, for a total of 3 distinct prime divisors, so 5 is in the list.

Mathematica

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

Crossrefs

Cf. A000984, A001221, A390327, A390328, A390329 (complement).

Sequence in context: A381537 A042956 A128217 * A393024 A288671 A378594

Adjacent sequences: A390327 A390328 A390329 * A390331 A390332 A390333

Keyword

nonn

Author

Clark Kimberling, Nov 01 2025

Status

approved