A363827 Highest power of 2 dividing n which is <= sqrt(n).

1, 1, 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, 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, 1, 2, 1, 8, 1, 2, 1, 4

Offset: 1

Author

Ilya Gutkovskiy, Oct 19 2023

Keywords

• easy
• nonn

Crossrefs

Cf. A006519, A033676, A135517, A363828.

Cf. A007814, A102572.

Programs

Mathematica

Table[Last[Select[Divisors[n], # <= Sqrt[n] && IntegerQ[Log[2, #]] &]], {n, 100}]
a[n_] := 2^Min[IntegerExponent[n, 2], Floor[Log2[n]/2]]; 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

Formula

a(n) = 2^min(A007814(n), A102572(n)). - Kevin Ryde, Oct 20 2023