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 A068310 n^2 - 1 divided by its largest square divisor. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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. a(n) = A005563(n-1) / A008833(n). [Reinhard Zumkeller, Nov 26 2011] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 2..10000 EXAMPLE a(6) = 35, as 6^2 - 1 = 35 itself is squarefree. 7^2-1 = 48, whose largest square divisor is 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 a(n) = A007913(n^2-1). Cf. A002350, 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

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Last modified January 17 01:29 EST 2021. Contains 340213 sequences. (Running on oeis4.)