A124676 a(n) = largest integer < n such that the positive integers <= a(n) and coprime to a(n) are also coprime to n.

1, 2, 2, 4, 2, 6, 6, 6, 4, 10, 6, 12, 6, 3, 14, 16, 12, 18, 10, 6, 10, 22, 18, 20, 12, 24, 14, 28, 2, 30, 30, 9, 16, 5, 30, 36, 18, 12, 30, 40, 6, 42, 22, 30, 22, 46, 42, 42, 40, 15, 26, 52, 48, 10, 42, 18, 28, 58, 30, 60, 30, 42, 62, 10, 6, 66, 34, 21, 4, 70, 66, 72, 36, 60, 38, 7, 12

Offset

2,2

Links

Michel Marcus, Table of n, a(n) for n = 2..5000

Example

The positive integers k, k <= 6, where the positive integers <= k and coprime to k are also coprime to 6, are 1,2,6. So a(6) = the largest of these < 6, which is 2.

Mathematica

f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[n_] := Select[Range[n - 1], Times @@ GCD[f[ # ], n] == 1 &]; Max /@ Table[g[n], {n, 2, 80}] (* Ray Chandler, Dec 24 2006 *)

Prog

(PARI) isok(k, n) = my(v=select(x->(gcd(x, k) == 1), [1..k])); for (i=1, #v, if (gcd(v[i], n) != 1, return(0))); return(1);
a(n) = forstep (k=n-1, 1, -1, if (isok(k, n), return (k))); \\ Michel Marcus, Oct 20 2025

Crossrefs

Cf. A126260, A073353.

Sequence in context: A360523 A358039 A171751 * A076249 A062170 A375386

Adjacent sequences: A124673 A124674 A124675 * A124677 A124678 A124679

Keyword

nonn

Author

Leroy Quet, Dec 24 2006

Extensions

Extended by Ray Chandler, Dec 24 2006

Status

approved