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A083549 Quotient if least common multiple (lcm) of cototient values of consecutive integers is divided by the greatest common divisor (gcd) of the same pair of consecutive numbers.

%I A083549 #13 Mar 17 2018 12:14:17
%S A083549 0,1,2,2,4,4,4,12,2,6,8,8,8,56,56,8,12,12,12,12,12,12,16,80,70,126,
%T A083549 144,16,22,22,16,208,234,198,264,24,20,12,40,24,30,30,24,56,56,24,32,
%U A083549 224,210,570,532,28,36,60,480,672,70,30,44,44,32,864,864,544,782,46,36,900
%N A083549 Quotient if least common multiple (lcm) of cototient values of consecutive integers is divided by the greatest common divisor (gcd) of the same pair of consecutive numbers.
%H A083549 Michael De Vlieger, <a href="/A083549/b083549.txt">Table of n, a(n) for n = 1..10000</a>
%F A083549 a(n) = lcm(A051953(n), A051952(n+1))/gcd(A051953(n), A051952(n+1)) = lcm(cototient(n+1), cototient(n))/A049586(n).
%e A083549 n=33: cototient(33) = 33-20 = 13, cototient(34) = 34-16 = 18;
%e A083549 lcm(13,18) = 234, gcd(13,18) = 1, so a(34) = 234.
%t A083549 f[x_] := x-EulerPhi[x]; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 69}]
%t A083549 (* Second program: *)
%t A083549 Map[Apply[LCM, #]/Apply[GCD, #] &@ Map[# - EulerPhi@ # &, #] &, Partition[Range[69], 2, 1]] (* _Michael De Vlieger_, Mar 17 2018 *)
%Y A083549 Cf. A051953, A083538, A083539, A083540, A083541, A083542, A083543, A083544, A083545, A083546, A083547, A083548, A083549, A083550, A083551, A083552, A083553, A083554, A083555, A049586.
%K A083549 nonn
%O A083549 1,3
%A A083549 _Labos Elemer_, May 22 2003