A068238 Denominators of arithmetic derivative of 1/n: -A003415(n)/n^2.

1, 4, 9, 4, 25, 36, 49, 16, 27, 100, 121, 9, 169, 196, 225, 8, 289, 108, 361, 50, 441, 484, 529, 144, 125, 676, 27, 49, 841, 900, 961, 64, 1089, 1156, 1225, 108, 1369, 1444, 1521, 400, 1681, 1764, 1849, 121, 675, 2116, 2209, 144, 343, 500, 2601, 338, 2809, 36

Offset: 1

Author

Reinhard Zumkeller, Feb 23 2002

Keywords

• nonn
• frac

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A068237 (numerators).

Programs

Maple

d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
a:= n-> denom(-d(n)/n^2):
seq(a(n), n=1..80);  # Alois P. Heinz, Jun 07 2015

Mathematica

d[n_] := If[n < 2, 0, n Sum[f[[2]]/f[[1]], {f, FactorInteger[n]}]];
a[n_] := Denominator[-d[n]/n^2];
Array[a, 80] (* Jean-François Alcover, Mar 12 2019 *)

Python

from fractions import Fraction
from sympy import factorint
def A068238(n): return Fraction(sum((Fraction(e,p) for p,e in factorint(n).items())),n).denominator # Chai Wah Wu, Nov 03 2022