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

1,3

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: A358290 A098930 A075372 * A301761 A253644 A100330

Adjacent sequences: A064722 A064723 A064724 * A064726 A064727 A064728

Keyword

easy,nonn

Author

Jason Earls, Oct 16 2001

Status

approved