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A375669
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The maximum exponent in the prime factorization of the largest odd divisor of n.
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2
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0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1
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OFFSET
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1,9
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COMMENTS
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The largest exponent among the exponents of the odd primes in the prime factorization of n.
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LINKS
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FORMULA
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a(n) = 0 if and only if n is a power of 2 (A000079).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} k * d(k) = 1.25979668632898014495... , where d(k) is the asymptotic density of the occurrences of k in this sequence: d(1) = 4/(3*zeta(2)), and d(k) = (1/zeta(k+1)) / (1-1/2^(k+1)) - (1/zeta(k)) / (1-1/2^k) for k >= 2.
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MATHEMATICA
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a[n_] := Module[{o = n / 2^IntegerExponent[n, 2]}, If[o == 1, 0, Max[FactorInteger[o][[;; , 2]]]]]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(o = n >> valuation(n, 2)); if(o == 1, 0, vecmax(factor(o)[, 2])); }
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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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