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A368472
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Product of exponents of prime factorization of the exponentially odd numbers.
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5
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1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1
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OFFSET
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1,7
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COMMENTS
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The first position of 2*k-1, for k = 1, 2, ..., is 1, 7, 24, 91, 154, 1444, 5777, 610, 92349, ..., which is the position of A085629(2*k-1) in A268335.
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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) = (zeta(2)^2/d) * Product_{p prime} (1 - 3/p^2 + 3/p^3 - 1/p^5) = 1.38446562720473484463..., where d = A065463 is the asymptotic density of the exponentially odd numbers.
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MATHEMATICA
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f[n_] := Module[{p = Times @@ FactorInteger[n][[;; , 2]]}, If[OddQ[p], p, Nothing]]; Array[f, 150]
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PROG
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(PARI) lista(kmax) = {my(p); for(k = 1, kmax, p = vecprod(factor(k)[, 2]); if(p%2, print1(p, ", "))); }
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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