A381972 Numbers k>=3 such that k/A001414(k) > (k-1)/A001414(k-1).

6, 8, 9, 12, 14, 15, 16, 18, 20, 24, 27, 30, 32, 35, 36, 38, 39, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 77, 78, 80, 81, 84, 87, 88, 90, 95, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 123, 124, 125, 126

Offset: 1

Author

Clark Kimberling, Mar 16 2025

Keywords

• nonn

Comments

1 <= a(n+1) - a(n) <= 10 for n = 2..3000000.

Examples

			f(2) = 1 < f(6) = 6/5 < f(8) = 4/3 < f(9) = 3/2 < f(12) = 12/7, where f(k) = k/A001414(k).
		

Crossrefs

Cf. A001414, A082299, A082343, A082344, A381249.

Programs

Mathematica

z = 200; f[n_] := FactorInteger[n];
g[n_] := Map[First, f[n]] . Map[Last, f[n]];
h[n_] := If[n/g[n] > (n - 1)/g[n - 1], n, 0];
Rest[Union[Table[h[n], {n, 2, z}]]]

Extensions

Definition corrected by Clark Kimberling, May 08 2025