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

1,3

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

Example

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

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 *)

Prog

(PARI) a(n) = vecsum(factor(fibonacci(n))[, 1]); \\ Michel Marcus, Oct 15 2019
(Magma) [&+PrimeDivisors(Fibonacci(n)):n in [1..48]]; // Marius A. Burtea, Oct 15 2019

Crossrefs

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

Sequence in context: A139044 A060442 A060385 * A113195 A069110 A238684

Adjacent sequences: A080645 A080646 A080647 * A080649 A080650 A080651

Keyword

nonn

Author

Joseph L. Pe, Feb 28 2003

Status

approved