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A375768
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The maximum exponent in the prime factorization of the numbers whose maximum exponent in their prime factorization is a Fibonacci number.
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3
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0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1
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OFFSET
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1,4
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COMMENTS
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First differs from A375766 at n = 2448.
All the terms are Fibonacci numbers by definition.
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (1/zeta(2) + Sum_{k>=3} (Fibonacci(k) * (1/zeta(Fibonacci(k)+1) - 1/zeta(Fibonacci(k)))) / d = 1.52660290991620063268..., where d = 1/zeta(4) + Sum_{k>=5} (1/zeta(Fibonacci(k)+1) - 1/zeta(Fibonacci(k))) = 0.94462177878047854647... is the density of A369939.
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MATHEMATICA
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fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; s[n_] := Module[{e = Max[FactorInteger[n][[;; , 2]]]}, If[fibQ[e], e, Nothing]]; s[1] = 0; Array[s, 100]
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PROG
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(PARI) isfib(n) = issquare(5*n^2 - 4) || issquare(5*n^2 + 4);
lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(isfib(e), print1(e, ", "))); }
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CROSSREFS
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KEYWORD
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nonn,easy,new
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AUTHOR
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STATUS
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approved
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