cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068237 Numerators of arithmetic derivative of 1/n: -A003415(n)/n^2.

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%I A068237 #18 Nov 03 2022 16:36:00
%S A068237 0,-1,-1,-1,-1,-5,-1,-3,-2,-7,-1,-1,-1,-9,-8,-1,-1,-7,-1,-3,-10,-13,
%T A068237 -1,-11,-2,-15,-1,-2,-1,-31,-1,-5,-14,-19,-12,-5,-1,-21,-16,-17,-1,
%U A068237 -41,-1,-3,-13,-25,-1,-7,-2,-9,-20,-7,-1,-1,-16,-23,-22,-31,-1,-23
%N A068237 Numerators of arithmetic derivative of 1/n: -A003415(n)/n^2.
%H A068237 Alois P. Heinz, <a href="/A068237/b068237.txt">Table of n, a(n) for n = 1..10000</a>
%p A068237 d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p A068237 a:= n-> numer(-d(n)/n^2):
%p A068237 seq(a(n), n=1..80);  # _Alois P. Heinz_, Jun 07 2015
%t A068237 d[n_] := If[n < 2, 0, n Sum[f[[2]]/f[[1]], {f, FactorInteger[n]}]];
%t A068237 a[n_] := Numerator[-d[n]/n^2];
%t A068237 Array[a, 80] (* _Jean-François Alcover_, Mar 12 2019 *)
%o A068237 (Python)
%o A068237 from fractions import Fraction
%o A068237 from sympy import factorint
%o A068237 def A068237(n): return -Fraction(sum((Fraction(e,p) for p,e in factorint(n).items())),n).numerator # _Chai Wah Wu_, Nov 03 2022
%Y A068237 Cf. A003415, A068238 (denominators).
%K A068237 sign,frac,look
%O A068237 1,6
%A A068237 _Reinhard Zumkeller_, Feb 23 2002