A060654 a(n) = gcd(n, A060766(n)).

1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 7, 11, 1, 12, 5, 13, 9, 14, 1, 30, 1, 16, 11, 17, 7, 18, 1, 19, 13, 20, 1, 21, 1, 22, 15, 23, 1, 24, 7, 25, 17, 26, 1, 27, 11, 28, 19, 29, 1, 60, 1, 31, 21, 32, 13, 33, 1, 34, 23, 70, 1, 36, 1, 37, 25, 38, 11, 39, 1, 40, 27, 41

Offset

2,3

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Formula

a(n) = gcd(n, lcm(dd(n))), where dd(n) is the first difference of divisors (ordered by size).

Example

If n is prime p, then A060766(p) = p-1 and lcm(p, p-1) = 1. If n=2k then a(2k)=k or as an "anomaly", a(2k)=2k.
At n=30, D={1, 2, 3, 5, 6, 10, 15, 30}, dD={1, 1, 2, 1, 4, 5, 15}={1, 2, 4, 5, 15}, lcm(dD)=60, gcd(n, lcm(dD(n))) = gcd(30, 60) = 30 = n.
At n=36, D={1, 2, 3, 4, 6, 9, 12, 18, 36}, dD={1, 1, 1, 2, 3, 3, 6, 18}={1, 2, 3, 6, 18}, lcm(dD)=18, gcd(n, lcm(dD(n))) = gcd(36, 18) = 18 = n/2.

Maple

A060766:= proc(n) local F; F:= sort(convert(numtheory:-divisors(n), list));
   ilcm(op(F[2..-1] - F[1..-2])) end proc:
seq(igcd(n, A060766(n)), n=2..100); # Robert Israel, Dec 20 2015

Mathematica

Table[GCD[n, LCM @@ Differences@ Divisors@ n], {n, 2, 82}] (* Michael De Vlieger, Dec 20 2015 *)

Crossrefs

Cf. A000005, A060680-A060685, A060741, A060742, A060763-A060766.

Sequence in context: A325563 A159353 A032742 * A291329 A291328 A280497

Adjacent sequences: A060651 A060652 A060653 * A060655 A060656 A060657

Keyword

nonn

Author

Labos Elemer, Apr 25 2001

Status

approved