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%I #34 Sep 23 2023 03:11:12
%S 3,2,15,6,35,3,7,5,11,30,143,42,195,14,255,2,323,10,399,110,483,33,23,
%T 39,3,182,87,210,899,15,1023,17,1155,34,1295,38,1443,95,1599,105,1763,
%U 462,215,506,235,138,47,6,51,26,2703,78,2915,21,3135,203,3363,870,3599
%N n^2 - 1 divided by its largest square divisor.
%C In other words, squarefree part of n^2-1.
%C Least m for which x^2 - m*y^2 = 1 has a solution with x = n.
%H Reinhard Zumkeller, <a href="/A068310/b068310.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A007913(n^2-1).
%F a(n) = A005563(n-1) / A008833(n^2 - 1)). [_Reinhard Zumkeller_, Nov 26 2011; corrected by _Georg Fischer_, Dec 10 2022]
%e a(6) = 35, as 6^2 - 1 = 35 itself is squarefree.
%e 7^2-1 = 48 = A005563(6), whose largest square divisor is A008833(48) = 16, so a(7) = 48/16 = 3.
%t a[n_] := Times@@(#[[1]] ^ Mod[ #[[2]], 2]&/@FactorInteger[n^2-1])
%t Table[(n^2-1)/Max[Select[Divisors[n^2-1],IntegerQ[Sqrt[#]]&]],{n,2,60}] (* _Harvey P. Dale_, Dec 08 2019 *)
%o (PARI) a(n) = core(n*n - 1); \\ _David Wasserman_, Mar 07 2005
%o (Haskell)
%o a068310 n = f 1 $ a027746_row (n^2 - 1) where
%o f y [] = y
%o f y [p] = y*p
%o f y (p:ps'@(p':ps)) | p == p' = f y ps
%o | otherwise = f (y*p) ps'
%o -- _Reinhard Zumkeller_, Nov 26 2011
%Y Cf. A002350, A007913, A067872, A033314, A027746, A175607.
%K easy,nice,nonn
%O 2,1
%A _Lekraj Beedassy_, Feb 25 2002
%E Edited by _Dean Hickerson_, Mar 19 2002
%E Entry revised by _N. J. A. Sloane_, Apr 27 2007
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