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A068329
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Arithmetic derivative of Fibonacci numbers > 0.
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3
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0, 0, 1, 1, 1, 12, 1, 10, 19, 16, 1, 384, 1, 42, 437, 491, 1, 4164, 150, 4388, 6341, 288, 1, 155472, 30035, 754, 115271, 142474, 1, 1530588, 2974, 1084624, 1802069, 5168, 2555363, 46594656, 503939, 1406531
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OFFSET
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1,6
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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
(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
(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
(Python)
from sympy import fibonacci, factorint
f = fibonacci(n)
return sum((f*e//p for p, e in factorint(f).items())) if n > 2 else 0 # Chai Wah Wu, Jun 12 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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