A363828 Highest power of 2 dividing n which is < sqrt(n), for n >= 2; a(1) = 1.
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4
Offset: 1
Keywords
Programs
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Mathematica
Join[{1}, Table[Last[Select[Divisors[n], # < Sqrt[n] && IntegerQ[Log[2, #]] &]], {n, 2, 100}]] a[n_] := 2^Min[IntegerExponent[n, 2], Ceiling[Log2[n]/2] - 1]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *) -
PARI
a(n) = if (n==1, 1, vecmax(select(x->((x^2 < n) && (2^logint(x,2)==x)), divisors(n)))); \\ Michel Marcus, Oct 19 2023