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A126773 a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.).

%I A126773 #12 Mar 03 2017 04:07:59
%S A126773 1,2,3,1,5,2,7,1,1,2,11,1,13,2,3,1,17,2,19,1,3,2,23,1,1,2,1,1,29,2,31,
%T A126773 1,3,2,5,1,37,2,3,1,41,2,43,1,1,2,47,1,1,2,3,1,53,2,5,1,3,2,59,1,61,2,
%U A126773 1,1,5,2,67,1,3,2,71,1,73,2,3,1,7,2,79,1,1,2,83,1,5,2,3,1,89,2,7,1,3,2,5,1
%N A126773 a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.).
%C A126773 Also the denominator of the ratio of the largest proper divisor to the least prime divisor of n, which can be thought of as the ratio of the 2nd largest divisor to the 2nd least divisor of n. - _Michel Marcus_, Feb 27 2017
%H A126773 Charles R Greathouse IV, <a href="/A126773/b126773.txt">Table of n, a(n) for n = 1..10000</a>
%F A126773 For n >= 2: Let p =A020639(n) be the smallest prime dividing n. If p^2 divides n, then a(n)=1. Otherwise, a(n) = p.
%e A126773 The largest proper divisor of 30 is A032742(30) = 15. So a(30)= 2, because 2 is the largest divisor of 30 which is coprime to 15.
%p A126773 A126773 := proc(n)
%p A126773     local p ;
%p A126773     p := A020639(n) ;
%p A126773     if modp(n,p^2) = 0 then
%p A126773         1 ;
%p A126773     else
%p A126773         p ;
%p A126773     end if;
%p A126773 end proc:
%p A126773 seq(A126773(n),n=1..100) ; # _R. J. Mathar_, Mar 03 2017
%t A126773 f[n_] := Block[{d = Divisors[n]},If[n < 2, 1, Max @@ Select[d, GCD[ #, d[[ -2]]] == 1 &]]];Array[f, 100] (* _Ray Chandler_, Feb 26 2007 *)
%o A126773 (PARI) a(n) = if (n==1, 1, my(d = divisors(n)); k = #d; while (gcd(d[k], d[#d-1]) != 1, k--); d[k]); \\ _Michel Marcus_, Feb 27 2017
%o A126773 (PARI) a(n) = if (n==1, 1, my(d = divisors(n)); denominator(d[#d-1]/d[2])); \\ _Michel Marcus_, Feb 27 2017
%o A126773 (PARI) a(n)=if(n==1, return(1)); my(f=factor(n)[1,]); if(f[2]>1, 1, f[1]) \\ _Charles R Greathouse IV_, Feb 27 2017
%K A126773 nonn
%O A126773 1,2
%A A126773 _Leroy Quet_, Feb 17 2007
%E A126773 Extended by _Ray Chandler_, Feb 26 2007