A358821 a(n) is the largest square dividing n^2 - 1.

1, 4, 1, 4, 1, 16, 9, 16, 9, 4, 1, 4, 1, 16, 1, 144, 1, 36, 1, 4, 1, 16, 25, 16, 225, 4, 9, 4, 1, 64, 1, 64, 1, 36, 1, 36, 1, 16, 1, 16, 1, 4, 9, 4, 9, 16, 49, 400, 49, 100, 1, 36, 1, 144, 1, 16, 1, 4, 1, 4, 9, 64, 9, 64, 1, 4, 1, 4, 1, 144, 1, 144, 25, 4

Offset: 2

Author

Darío Clavijo, Jan 04 2023

Keywords

• nonn

Crossrefs

Cf. A007913, A008833, A068310, A005563.

Programs

Mathematica

f[p_, e_] := p^(2*Floor[e/2]); a[n_] := Times @@ (f @@@ FactorInteger[n^2 - 1]); Array[a, 100, 2] (* Amiram Eldar, Jan 04 2023 *)

PARI

a(n) = (n^2-1)/core(n^2-1); \\ Michel Marcus, Feb 19 2023

Python

from sympy.ntheory.factor_ import core
def a(n):
  return (n**2-1)//core(n**2-1)

Formula

a(n) = A008833(n^2 - 1).

a(n) = A008833(A005563(n-1)).

a(n) = A005563(n-1) / A068310(n).

a(n) = A005563(n-1) / A007913(A005563(n-1)).

a(n) = (n^2 - 1) / A068310(n).

a(n) = (n^2 - 1) / A007913(n^2 - 1).