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A064725
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Sum of primes dividing Fibonacci(n) (with repetition).
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3
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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
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OFFSET
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1,3
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..350
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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fiboPrimeFactorSum[n_] := Plus @@ Times @@@ FactorInteger@ Fibonacci[n]; fiboPrimeFactorSum[1] = 0; Array[fiboPrimeFactorSum, 60] (* Michel Lagneau, Nov 13 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A000045, A001414, A080648 (without repetition).
Sequence in context: A191783 A098930 A075372 * A100330 A020473 A098833
Adjacent sequences: A064722 A064723 A064724 * A064726 A064727 A064728
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KEYWORD
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easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Oct 16 2001
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STATUS
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approved
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