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

1,4

Links

Table of n, a(n) for n=1..100.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A006519, A033676, A135517, A363828.

Cf. A007814, A102572.

Sequence in context: A161265 A161290 A185218 * A161317 A161251 A161036

Adjacent sequences: A363824 A363825 A363826 * A363828 A363829 A363830

Keyword

easy,nonn

Author

Ilya Gutkovskiy, Oct 19 2023

Status

approved