cp's OEIS Frontend

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

%I A068238 #15 Nov 03 2022 16:35:52
%S A068238 1,4,9,4,25,36,49,16,27,100,121,9,169,196,225,8,289,108,361,50,441,
%T A068238 484,529,144,125,676,27,49,841,900,961,64,1089,1156,1225,108,1369,
%U A068238 1444,1521,400,1681,1764,1849,121,675,2116,2209,144,343,500,2601,338,2809,36
%N A068238 Denominators of arithmetic derivative of 1/n: -A003415(n)/n^2.
%H A068238 Alois P. Heinz, <a href="/A068238/b068238.txt">Table of n, a(n) for n = 1..10000</a>
%p A068238 d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p A068238 a:= n-> denom(-d(n)/n^2):
%p A068238 seq(a(n), n=1..80);  # _Alois P. Heinz_, Jun 07 2015
%t A068238 d[n_] := If[n < 2, 0, n Sum[f[[2]]/f[[1]], {f, FactorInteger[n]}]];
%t A068238 a[n_] := Denominator[-d[n]/n^2];
%t A068238 Array[a, 80] (* _Jean-François Alcover_, Mar 12 2019 *)
%o A068238 (Python)
%o A068238 from fractions import Fraction
%o A068238 from sympy import factorint
%o A068238 def A068238(n): return Fraction(sum((Fraction(e,p) for p,e in factorint(n).items())),n).denominator # _Chai Wah Wu_, Nov 03 2022
%Y A068238 Cf. A003415, A068237 (numerators).
%K A068238 nonn,frac
%O A068238 1,2
%A A068238 _Reinhard Zumkeller_, Feb 23 2002