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.

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, 144, 16, 22, 22, 16, 208, 234, 198, 264, 24, 20, 12, 40, 24, 30, 30, 24, 56, 56, 24, 32, 224, 210, 570, 532, 28, 36, 60, 480, 672, 70, 30, 44, 44, 32, 864, 864, 544, 782, 46, 36, 900

Offset: 1

Author

Labos Elemer, May 22 2003

Keywords

• nonn

Examples

			n=33: cototient(33) = 33-20 = 13, cototient(34) = 34-16 = 18;
lcm(13,18) = 234, gcd(13,18) = 1, so a(34) = 234.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

f[x_] := x-EulerPhi[x]; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 69}]
(* Second program: *)
Map[Apply[LCM, #]/Apply[GCD, #] &@ Map[# - EulerPhi@ # &, #] &, Partition[Range[69], 2, 1]] (* Michael De Vlieger, Mar 17 2018 *)

Formula

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