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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.
1

%I #13 Mar 17 2018 12:14:17

%S 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 144,16,22,22,16,208,234,198,264,24,20,12,40,24,30,30,24,56,56,24,32,

%U 224,210,570,532,28,36,60,480,672,70,30,44,44,32,864,864,544,782,46,36,900

%N 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 Michael De Vlieger, <a href="/A083549/b083549.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = lcm(A051953(n), A051952(n+1))/gcd(A051953(n), A051952(n+1)) = lcm(cototient(n+1), cototient(n))/A049586(n).

%e n=33: cototient(33) = 33-20 = 13, cototient(34) = 34-16 = 18;

%e lcm(13,18) = 234, gcd(13,18) = 1, so a(34) = 234.

%t f[x_] := x-EulerPhi[x]; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 69}]

%t (* Second program: *)

%t Map[Apply[LCM, #]/Apply[GCD, #] &@ Map[# - EulerPhi@ # &, #] &, Partition[Range[69], 2, 1]] (* _Michael De Vlieger_, Mar 17 2018 *)

%Y Cf. A051953, A083538, A083539, A083540, A083541, A083542, A083543, A083544, A083545, A083546, A083547, A083548, A083549, A083550, A083551, A083552, A083553, A083554, A083555, A049586.

%K nonn

%O 1,3

%A _Labos Elemer_, May 22 2003