|
%I #38 Feb 25 2024 05:58:22
%S 0,0,1,1,1,12,1,10,19,16,1,384,1,42,437,491,1,4164,150,4388,6341,288,
%T 1,155472,30035,754,115271,142474,1,1530588,2974,1084624,1802069,5168,
%U 2555363,46594656,503939,1406531
%N Arithmetic derivative of Fibonacci numbers > 0.
%H 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 a(n) = A003415(A000045(n)).
%t 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 (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 (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 (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 (Python)
%o from sympy import fibonacci, factorint
%o def A068329(n):
%o f = fibonacci(n)
%o return sum((f*e//p for p,e in factorint(f).items())) if n > 2 else 0 # _Chai Wah Wu_, Jun 12 2022
%Y Cf. A000045, A003415, A001605 (where a(n) = 1).
%K nonn
%O 1,6
%A _Reinhard Zumkeller_, Feb 27 2002
|
