A376554 Square root of largest unitary square divisor of binomial(n, floor(n/2)).

1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 2, 2, 1, 3, 3, 1, 2, 1, 2, 2, 1, 1, 2, 10, 5, 10, 5, 3, 12, 3, 3, 1, 2, 5, 10, 10, 5, 3, 6, 2, 1, 2, 1, 5, 20, 15, 30, 42, 21, 14, 7, 7, 28, 2, 1, 1, 4, 1, 4, 4, 1, 21, 21, 7, 14, 7, 14, 6, 3, 1, 2, 2, 1, 10, 5, 35, 140, 7, 14

Offset: 0

Author

Amiram Eldar, Sep 28 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001405, A071974, A376553, A376555, A376556.

Programs

Mathematica

f[p_, e_] := If[EvenQ[e], p^(e/2), 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[Binomial[n, Floor[n/2]]]; Array[a, 100, 0]

PARI

a(n) = {my(f = factor(binomial(n, n\2))); prod(i = 1, #f~, if(f[i, 2]%2, 1, f[i, 1]^(f[i, 2]/2)));}

Formula

a(n) = A071974(A001405(n)).

a(n) = sqrt(A376553(n)).