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A214720 Least m>0 such that n^2-m and n-m are relatively prime.

%I A214720 #11 Mar 30 2014 12:13:32
%S A214720 2,1,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,
%T A214720 2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,2,5,2,3,
%U A214720 2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2
%N A214720 Least m>0 such that n^2-m and n-m are relatively prime.
%H A214720 Clark Kimberling, <a href="/A214720/b214720.txt">Table of n, a(n) for n = 1..1000</a>
%e A214720 a(12) = 5 because of the following:
%e A214720 gcd(144-1,11) > 1,
%e A214720 gcd(144-2,10) > 1 ,
%e A214720 gcd(144-3,9) > 1,
%e A214720 gcd(144-4,8) >1,
%e A214720 gcd(144-5,7) = 1.
%p A214720 A214720 := proc(n)
%p A214720     for m from 1 do
%p A214720         if igcd(n^2-m,n-m) =1  then
%p A214720             return m;
%p A214720         end if;
%p A214720     end do:
%p A214720 end proc: # _R. J. Mathar_, Mar 30 2014
%t A214720 Table[m = 1; While[GCD[5^n - m, n - m] != 1, m++]; m, {n, 1, 140}]
%Y A214720 Cf. A214716, A053669.
%K A214720 nonn,easy
%O A214720 1,1
%A A214720 _Clark Kimberling_, Jul 27 2012