A381249 Indices of records in k/A001414(k), k>=2.

2, 6, 8, 9, 12, 15, 16, 18, 24, 27, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 81, 90, 96, 108, 120, 128, 135, 144, 160, 162, 180, 192, 216, 240, 243, 270, 288, 320, 324, 360, 384, 405, 432, 480, 486, 540, 576, 640, 648, 720, 729, 810, 864, 960, 972, 1024, 1080, 1152

Offset: 1

Author

Clark Kimberling, Apr 19 2025

Keywords

• nonn

Comments

Except for initial 2, this is a subsequence of A381972.

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, A381972.

Programs

Mathematica

z = 800; g[n_] := FactorInteger[n];
f[n_] := Map[First, g[n]] . Map[Last, g[n]];
mx = -1; k = 2; u = {}; While[k < z, a = k/f[k]; If[a > mx, mx = a; AppendTo[u, k]]; k++]; u

PARI

sopfr(n) = (n=factor(n))[, 1]~*n[, 2];
lista(nn) = my(r=oo, list=List()); for (n=2, nn, my(x=sopfr(n)/n); if (x < r, listput(list, n); r = x)); Vec(list); \\ Michel Marcus, Apr 27 2025

Extensions

More terms from Michel Marcus, Apr 27 2025