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

2,2

Links

Table of n, a(n) for n=2..75.

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).

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 *)

Prog

(Python)
from sympy.ntheory.factor_ import core
def a(n):
  return (n**2-1)//core(n**2-1)
(PARI) a(n) = (n^2-1)/core(n^2-1); \\ Michel Marcus, Feb 19 2023

Crossrefs

Cf. A007913, A008833, A068310, A005563.

Sequence in context: A077088 A376132 A348971 * A297420 A156896 A375743

Adjacent sequences: A358818 A358819 A358820 * A358822 A358823 A358824

Keyword

nonn

Author

Darío Clavijo, Jan 04 2023

Status

approved