A390329 Numbers k such that the number of distinct prime divisors of binomial(2k, k) is even.

2, 3, 6, 7, 11, 12, 13, 14, 16, 17, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 39, 42, 43, 44, 48, 49, 50, 51, 52, 54, 58, 59, 64, 65, 67, 72, 73, 74, 77, 78, 79, 86, 87, 88, 89, 90, 92, 96, 97, 99, 102, 103, 109, 110, 126, 133, 134, 135

Offset

1,1

Links

Table of n, a(n) for n=1..63.

Example

Binomial(14,7) = (2^3)*3*11*13, for a total of 4 distinct prime divisors, so 7 is in the list.

Mathematica

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

Crossrefs

Cf. A000984, A001221, A067434, A390327, A390328, A390330 (complement).

Sequence in context: A375738 A396190 A253239 * A226384 A298947 A075995

Adjacent sequences: A390326 A390327 A390328 * A390330 A390331 A390332

Keyword

nonn

Author

Clark Kimberling, Nov 01 2025

Status

approved