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.
%I A068329 #38 Feb 25 2024 05:58:22 %S A068329 0,0,1,1,1,12,1,10,19,16,1,384,1,42,437,491,1,4164,150,4388,6341,288, %T A068329 1,155472,30035,754,115271,142474,1,1530588,2974,1084624,1802069,5168, %U A068329 2555363,46594656,503939,1406531 %N A068329 Arithmetic derivative of Fibonacci numbers > 0. %H A068329 Iain Fox, <a href="/A068329/b068329.txt">Table of n, a(n) for n = 1..400</a> (first 200 terms from T. D. Noe) %F A068329 a(n) = A003415(A000045(n)). %t A068329 ad[1] = 0; ad[n_] := Module[{f = FactorInteger[n]}, Total[n*f[[All, 2]]/ f[[All, 1]]]]; a[n_] := ad[Fibonacci[n]]; Array[a, 40] (* _Jean-François Alcover_, Feb 22 2018 *) %o A068329 (Magma) Ad:=func<h | h*(&+[Factorisation(h)[i][2]/Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; [n le 2 select 0 else Ad(Fibonacci(n)): n in [1..40]]; // _Bruno Berselli_, Oct 22 2013 %o A068329 (PARI) a(n) = my(f = factor(n=fibonacci(n))~); sum(i=1, #f, n/f[1, i]*f[2, i]) \\ _Iain Fox_, Oct 29 2018 %o A068329 (GAP) a:=Concatenation([0,0],List(List([3..40],n->Factors(Fibonacci(n))),i->Product(i)*Sum(i,j->1/j))); # _Muniru A Asiru_, Oct 31 2018 %o A068329 (Python) %o A068329 from sympy import fibonacci, factorint %o A068329 def A068329(n): %o A068329 f = fibonacci(n) %o A068329 return sum((f*e//p for p,e in factorint(f).items())) if n > 2 else 0 # _Chai Wah Wu_, Jun 12 2022 %Y A068329 Cf. A000045, A003415, A001605 (where a(n) = 1). %K A068329 nonn %O A068329 1,6 %A A068329 _Reinhard Zumkeller_, Feb 27 2002