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A064725 Sum of primes dividing Fibonacci(n) (with repetition). 3
0, 0, 2, 3, 5, 6, 13, 10, 19, 16, 89, 14, 233, 42, 68, 57, 1597, 42, 150, 60, 436, 288, 28657, 46, 3011, 754, 181, 326, 514229, 114, 2974, 2264, 19892, 5168, 141979, 160, 2443, 9499, 135956, 2228, 62158, 680, 433494437, 641, 109526, 29257, 2971215073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..350 from Harry J. Smith)

EXAMPLE

a(12) = 14 because Fibonacci(12) = 144 =  2^4*3^2 and the sum of the prime divisors with repetition is 4*2 + 2*3 = 14.

MAPLE

with (numtheory):with(combinat, fibonacci):

sopfr:= proc(n) local e, j; e := ifactors(fibonacci(n))[2]:

add (e[j][1]*e[j][2], j=1..nops(e)) end:

seq (sopfr(n), n=1..100); # Michel Lagneau, Nov 13 2012

# second Maple program:

a:= n-> add(i[1]*i[2], i=ifactors((<<0|1>, <1|1>>^n)[1, 2])[2]):

seq(a(n), n=1..47);  # Alois P. Heinz, Sep 03 2019

MATHEMATICA

fiboPrimeFactorSum[n_] := Plus @@ Times @@@ FactorInteger@ Fibonacci[n]; fiboPrimeFactorSum[1] = 0; Array[fiboPrimeFactorSum, 60] (* Michel Lagneau, Nov 13 2012 *)

PROG

(PARI) sopfr(n)= { local(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]*f[i, 2]); return(s) } { for (n = 0, 350, write("b064725.txt", n, " ", sopfr(fibonacci(n))) ) } \\ Harry J. Smith, Sep 23 2009

CROSSREFS

Cf. A000045, A001414, A080648 (without repetition).

Sequence in context: A191783 A098930 A075372 * A301761 A253644 A100330

Adjacent sequences:  A064722 A064723 A064724 * A064726 A064727 A064728

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Oct 16 2001

STATUS

approved

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Last modified September 27 18:31 EDT 2021. Contains 347694 sequences. (Running on oeis4.)