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A068310
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n^2 - 1 divided by its largest square divisor.
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7
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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
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OFFSET
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2,1
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COMMENTS
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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]
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Lekraj Beedassy, Feb 25 2002
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EXTENSIONS
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Edited by Dean Hickerson, Mar 19 2002
Entry revised by N. J. A. Sloane, Apr 27 2007
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STATUS
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approved
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