|
%I #20 Dec 23 2015 02:34:36
%S 1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10,7,11,1,12,5,13,9,14,1,30,1,16,
%T 11,17,7,18,1,19,13,20,1,21,1,22,15,23,1,24,7,25,17,26,1,27,11,28,19,
%U 29,1,60,1,31,21,32,13,33,1,34,23,70,1,36,1,37,25,38,11,39,1,40,27,41
%N a(n) = gcd(n, A060766(n)).
%H Robert Israel, <a href="/A060654/b060654.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = gcd(n, lcm(dd(n))), where dd(n) is the first difference of divisors (ordered by size).
%e If n is prime p, then A060766(p) = p-1 and lcm(p, p-1) = 1. If n=2k then a(2k)=k or as an "anomaly", a(2k)=2k.
%e At n=30, D={1, 2, 3, 5, 6, 10, 15, 30}, dD={1, 1, 2, 1, 4, 5, 15}={1, 2, 4, 5, 15}, lcm(dD)=60, gcd(n, lcm(dD(n))) = gcd(30, 60) = 30 = n.
%e At n=36, D={1, 2, 3, 4, 6, 9, 12, 18, 36}, dD={1, 1, 1, 2, 3, 3, 6, 18}={1, 2, 3, 6, 18}, lcm(dD)=18, gcd(n, lcm(dD(n))) = gcd(36, 18) = 18 = n/2.
%p A060766:= proc(n) local F; F:= sort(convert(numtheory:-divisors(n),list));
%p ilcm(op(F[2..-1] - F[1..-2])) end proc:
%p seq(igcd(n,A060766(n)),n=2..100); # _Robert Israel_, Dec 20 2015
%t Table[GCD[n, LCM @@ Differences@ Divisors@ n], {n, 2, 82}] (* _Michael De Vlieger_, Dec 20 2015 *)
%Y Cf. A000005, A060680-A060685, A060741, A060742, A060763-A060766.
%K nonn
%O 2,3
%A _Labos Elemer_, Apr 25 2001
|
