A068310 n^2 - 1 divided by its largest square divisor.

3, 2, 15, 6, 35, 3, 7, 5, 11, 30, 143, 42, 195, 14, 255, 2, 323, 10, 399, 110, 483, 33, 23, 39, 3, 182, 87, 210, 899, 15, 1023, 17, 1155, 34, 1295, 38, 1443, 95, 1599, 105, 1763, 462, 215, 506, 235, 138, 47, 6, 51, 26, 2703, 78, 2915, 21, 3135, 203, 3363, 870, 3599

Offset

2,1

Comments

In other words, squarefree part of n^2-1.

Least m for which x^2 - m*y^2 = 1 has a solution with x = n.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Formula

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

a(n) = A005563(n-1) / A008833(n^2 - 1)). [Reinhard Zumkeller, Nov 26 2011; corrected by Georg Fischer, Dec 10 2022]

Example

a(6) = 35, as 6^2 - 1 = 35 itself is squarefree.
7^2-1 = 48 = A005563(6), whose largest square divisor is A008833(48) = 16, so a(7) = 48/16 = 3.

Mathematica

a[n_] := Times@@(#[[1]] ^ Mod[ #[[2]], 2]&/@FactorInteger[n^2-1])
Table[(n^2-1)/Max[Select[Divisors[n^2-1], IntegerQ[Sqrt[#]]&]], {n, 2, 60}] (* Harvey P. Dale, Dec 08 2019 *)

Prog

(PARI) a(n) = core(n*n - 1); \\ David Wasserman, Mar 07 2005
(Haskell)
a068310 n = f 1 $ a027746_row (n^2 - 1) where
   f y [] = y
   f y [p] = y*p
   f y (p:ps'@(p':ps)) | p == p' = f y ps
                       | otherwise = f (y*p) ps'
-- Reinhard Zumkeller, Nov 26 2011

Crossrefs

Cf. A002350, A007913, A067872, A033314, A027746, A175607.

Sequence in context: A328282 A332215 A086485 * A033314 A070260 A142705

Adjacent sequences: A068307 A068308 A068309 * A068311 A068312 A068313

Keyword

easy,nice,nonn

Author

Lekraj Beedassy, Feb 25 2002

Extensions

Edited by Dean Hickerson, Mar 19 2002

Entry revised by N. J. A. Sloane, Apr 27 2007

Status

approved