login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080648 Sum of prime factors of Fibonacci(n). 5
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)