A060695 a(n) = gcd(2n, A060766(2n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 30, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 60, 31, 32, 33, 34, 70, 36, 37, 38, 39, 40, 41, 42, 43, 44, 90, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 126, 64, 65, 66, 67, 68, 69, 140, 71

Offset: 1

Author

Labos Elemer, Apr 25 2001

Keywords

• nonn

Examples

			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
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.
		

Crossrefs

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

Programs

Mathematica

Table[GCD[2 n, LCM @@ Differences@ Divisors[2 n]], {n, 71}] (* Michael De Vlieger, Dec 20 2015 *)

PARI

a(n) = my(d=divisors(2*n), dd = vector(#d-1, k, d[k+1] - d[k])); gcd(2*n, lcm(dd)); \\ Michel Marcus, Mar 22 2020

Formula

a(n) = a(2k) is either n = 2k or n/2 = k. a(n) = n/2 seems regular, a(n) = n seems "anomalous".