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A080648 Sum of prime factors of Fibonacci(n).

%I A080648 #27 Sep 08 2022 08:45:09
%S A080648 0,0,2,3,5,2,13,10,19,16,89,5,233,42,68,57,1597,38,150,60,436,288,
%T A080648 28657,35,3006,754,181,326,514229,110,2974,2264,19892,5168,141979,148,
%U A080648 2443,9499,135956,2228,62158,676,433494437,641,109526,29257,2971215073,1185
%N A080648 Sum of prime factors of Fibonacci(n).
%H A080648 Amiram Eldar, <a href="/A080648/b080648.txt">Table of n, a(n) for n = 1..1408</a> (terms 1..1000 from T. D. Noe, using Blair Kelly's data)
%H A080648 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%e A080648 a(8) = 10 because Fibonacci(8) = 21 and the sum of the prime divisors {3, 7} equals 10.
%p A080648 with (numtheory):with(combinat, fibonacci):
%p A080648 sopf:= proc(n) local e, j; e := ifactors(fibonacci(n))[2]:
%p A080648 add (e[j][1], j=1..nops(e)) end:
%p A080648 seq (sopf(n), n=1..100); # _Michel Lagneau_, Nov 13 2012
%p A080648 A080648 := proc(n)
%p A080648     A008472(combinat[fibonacci](n)) ;
%p A080648 end proc: # _R. J. Mathar_, Nov 15 2012
%p A080648 # third Maple program:
%p A080648 a:= n-> add(i[1], i=ifactors((<<0|1>, <1|1>>^n)[1, 2])[2]):
%p A080648 seq(a(n), n=1..48);  # _Alois P. Heinz_, Sep 03 2019
%t A080648 Table[Apply[Plus, Transpose[FactorInteger[Fibonacci[n]]][[1]]], {n, 3, 100}] (* Pe *)
%t A080648 Array[Plus@@First/@FactorInteger[Fibonacci[ # ]]&, 40 ] (* _Michel Lagneau_, Nov 13 2012 *)
%o A080648 (PARI) a(n) = vecsum(factor(fibonacci(n))[,1]); \\ _Michel Marcus_, Oct 15 2019
%o A080648 (Magma) [&+PrimeDivisors(Fibonacci(n)):n in [1..48]]; // _Marius A. Burtea_, Oct 15 2019
%Y A080648 Cf. A000045, A008472, A060442 (Fibonacci prime factors).
%K A080648 nonn
%O A080648 1,3
%A A080648 _Joseph L. Pe_, Feb 28 2003