A080648 Sum of prime factors of Fibonacci(n).

0, 0, 2, 3, 5, 2, 13, 10, 19, 16, 89, 5, 233, 42, 68, 57, 1597, 38, 150, 60, 436, 288, 28657, 35, 3006, 754, 181, 326, 514229, 110, 2974, 2264, 19892, 5168, 141979, 148, 2443, 9499, 135956, 2228, 62158, 676, 433494437, 641, 109526, 29257, 2971215073, 1185

Offset: 1

Author

Joseph L. Pe, Feb 28 2003

Keywords

• nonn

Examples

			a(8) = 10 because Fibonacci(8) = 21 and the sum of the prime divisors {3, 7} equals 10.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1408 (terms 1..1000 from T. D. Noe, using Blair Kelly's data)
• Blair Kelly, Fibonacci and Lucas Factorizations

Crossrefs

Cf. A000045, A008472, A060442 (Fibonacci prime factors).

Programs

Magma

[&+PrimeDivisors(Fibonacci(n)):n in [1..48]]; // Marius A. Burtea, Oct 15 2019

Maple

with (numtheory):with(combinat, fibonacci):
sopf:= proc(n) local e, j; e := ifactors(fibonacci(n))[2]:
add (e[j][1], j=1..nops(e)) end:
seq (sopf(n), n=1..100); # Michel Lagneau, Nov 13 2012
A080648 := proc(n)
    A008472(combinat[fibonacci](n)) ;
end proc: # R. J. Mathar, Nov 15 2012
# third Maple program:
a:= n-> add(i[1], i=ifactors((<<0|1>, <1|1>>^n)[1, 2])[2]):
seq(a(n), n=1..48);  # Alois P. Heinz, Sep 03 2019

Mathematica

Table[Apply[Plus, Transpose[FactorInteger[Fibonacci[n]]][[1]]], {n, 3, 100}] (* Pe *)
Array[Plus@@First/@FactorInteger[Fibonacci[ # ]]&, 40 ] (* Michel Lagneau, Nov 13 2012 *)

PARI

a(n) = vecsum(factor(fibonacci(n))[,1]); \\ Michel Marcus, Oct 15 2019