A375669 The maximum exponent in the prime factorization of the largest odd divisor of n.
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
Offset: 1
Links
Programs
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Mathematica
a[n_] := Module[{o = n / 2^IntegerExponent[n, 2]}, If[o == 1, 0, Max[FactorInteger[o][[;;, 2]]]]]; Array[a, 100] -
PARI
a(n) = {my(o = n >> valuation(n, 2)); if(o == 1, 0, vecmax(factor(o)[,2]));}
Formula
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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