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

1,3

Links

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

Formula

a(n) = lcm(A051953(n), A051953(n+1)) / gcd(A051953(n), A051953(n+1)) = lcm(cototient(n+1), cototient(n)) / A049586(n). [Corrected by Sean A. Irvine, Feb 05 2026]

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A354492 A320195 A129163 * A083548 A376944 A082849

Adjacent sequences: A083546 A083547 A083548 * A083550 A083551 A083552

Keyword

nonn

Author

Labos Elemer, May 22 2003

Status

approved