A376553 Largest unitary square divisor of binomial(n, floor(n/2)).

1, 1, 1, 1, 1, 1, 4, 1, 1, 9, 36, 1, 4, 4, 1, 9, 9, 1, 4, 1, 4, 4, 1, 1, 4, 100, 25, 100, 25, 9, 144, 9, 9, 1, 4, 25, 100, 100, 25, 9, 36, 4, 1, 4, 1, 25, 400, 225, 900, 1764, 441, 196, 49, 49, 784, 4, 1, 1, 16, 1, 16, 16, 1, 441, 441, 49, 196, 49, 196, 36, 9

Offset

0,7

Links

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

Formula

a(n) = A350388(A001405(n)).

a(n) = A376554(n)^2.

Mathematica

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

Prog

(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])); }

Crossrefs

Cf. A001405, A350388, A376554, A376555, A376556.

Sequence in context: A243608 A219207 A157108 * A056647 A056057 A226234

Adjacent sequences: A376550 A376551 A376552 * A376554 A376555 A376556

Keyword

nonn

Author

Amiram Eldar, Sep 28 2024

Status

approved