A064725 Sum of primes dividing Fibonacci(n) (with repetition).

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

Offset: 1

Author

Jason Earls, Oct 16 2001

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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