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

%I A064725 #30 Apr 13 2024 14:57:03
%S A064725 0,0,2,3,5,6,13,10,19,16,89,14,233,42,68,57,1597,42,150,60,436,288,
%T A064725 28657,46,3011,754,181,326,514229,114,2974,2264,19892,5168,141979,160,
%U A064725 2443,9499,135956,2228,62158,680,433494437,641,109526,29257,2971215073
%N A064725 Sum of primes dividing Fibonacci(n) (with repetition).
%H A064725 Amiram Eldar, <a href="/A064725/b064725.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..350 from Harry J. Smith)
%e A064725 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.
%p A064725 with (numtheory):with(combinat, fibonacci):
%p A064725 sopfr:= proc(n) local e, j; e := ifactors(fibonacci(n))[2]:
%p A064725 add (e[j][1]*e[j][2], j=1..nops(e)) end:
%p A064725 seq (sopfr(n), n=1..100); # _Michel Lagneau_, Nov 13 2012
%p A064725 # second Maple program:
%p A064725 a:= n-> add(i[1]*i[2], i=ifactors((<<0|1>, <1|1>>^n)[1, 2])[2]):
%p A064725 seq(a(n), n=1..47);  # _Alois P. Heinz_, Sep 03 2019
%t A064725 fiboPrimeFactorSum[n_] := Plus @@ Times @@@ FactorInteger@ Fibonacci[n]; fiboPrimeFactorSum[1] = 0; Array[fiboPrimeFactorSum, 60] (* _Michel Lagneau_, Nov 13 2012 *)
%o A064725 (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) }
%o A064725 { for (n = 0, 350, write("b064725.txt", n, " ", sopfr(fibonacci(n))) ) } \\ _Harry J. Smith_, Sep 23 2009
%Y A064725 Cf. A000045, A001414, A080648 (without repetition).
%K A064725 nonn
%O A064725 1,3
%A A064725 _Jason Earls_, Oct 16 2001