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%I #22 Mar 18 2018 09:49:03
%S 1,1,1,1,1,4,1,6,6,24,1,360,1,120,180,420,1,1680,1,5040,1260,5040,1,
%T 55440,60,55440,2520,720720,1,10810800,1,360360,83160,1441440,2100,
%U 73513440,1,24504480,1081080,2327925600,1,1396755360,1,465585120,5405400,465585120,1,32125373280,420,10708457760,36756720,53542288800,1
%N LCM of numbers m such that 1 <= m <= n, m has a common factor with n, but m does not divide n.
%C From _Michael De Vlieger_, Oct 30 2017: (Start)
%C a(p) = 1 and a(4) = 1, since all 1 <= m <= 4 either divide or are coprime to 4 and 4 is the smallest composite.
%C a(n) > 1 for composite n > 4.
%C There are 2 species of m. The first is m | n^e with e >= 2, the second is m that is the product of at least one prime p | n (A272618) and one prime q coprime to n (A272619). Both species of m are composite. We can simply look for composite m in the cototient of n such that m does not divide n.
%C (End)
%C This isn't a subsequence of A025487. - _David A. Corneth_, Oct 30 2017
%H Antti Karttunen, <a href="/A066575/b066575.txt">Table of n, a(n) for n = 1..1024</a>
%F a(n) = lcm_{k} A133995(n,k). - _Michael De Vlieger_, Oct 30 2017
%e a(12) = 360 = lcm(8,9,10) as 8, 9 and 10 are the only numbers <= 12 which are not relatively prime to 12 nor do they divide 12.
%p for i from 1 to 100 do a := 1:for j from 1 to i do b := igcd(i,j); if(b>1 and b<j) then a := ilcm(a,j):end if:end do:c[i] := a; end do:q := seq(c[k],k=1..100);
%t Table[Apply[LCM, Select[Range[2, n - 1], Nor[Divisible[n, #], CoprimeQ[n, #]] &] /. {} -> 1], {n, 53}] (* _Michael De Vlieger_, Oct 30 2017 *)
%o (PARI) A066575(n) = { my(m=1); for(k=1,n,if((n%k)&&(gcd(n,k)>1),m = lcm(m,k))); m; }; \\ _Antti Karttunen_, Oct 30 2017
%Y Cf. A025487, A045763, A133995.
%K nonn
%O 1,6
%A _Amarnath Murthy_, Dec 19 2001
%E More terms from _Sascha Kurz_, Mar 23 2002 and from _Antti Karttunen_, Oct 30 2017
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