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A068238
Denominators of arithmetic derivative of 1/n: -A003415(n)/n^2.
3
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
1,2
LINKS
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 *)
PROG
(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
CROSSREFS
Cf. A003415, A068237 (numerators).
Sequence in context: A087320 A087321 A053143 * A280441 A255290 A087369
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Feb 23 2002
STATUS
approved