A328176 a(n) is the maximal value of the expression d AND (n/d) where d runs through the divisors of n and AND denotes the bitwise AND operator.

1, 0, 1, 2, 1, 2, 1, 0, 3, 0, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 3, 2, 1, 4, 5, 0, 1, 4, 1, 4, 1, 0, 3, 0, 5, 6, 1, 2, 1, 0, 1, 6, 1, 2, 3, 2, 1, 4, 7, 0, 1, 4, 1, 2, 1, 4, 3, 0, 1, 4, 1, 2, 1, 8, 5, 2, 1, 2, 3, 4, 1, 8, 1, 0, 5, 2, 3, 4, 1, 8, 9, 0, 1, 6, 1, 2, 1

Offset: 1

Author

Rémy Sigrist, Oct 06 2019

Keywords

• nonn
• base

Examples

			For n = 12:
- we have the following values:
    d   12/d  d AND (12/d)
    --  ----  ------------
     1    12             0
     2     6             2
     3     4             0
     4     3             0
     6     2             2
    12     1             0
- hence a(12) = max({0, 2}) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..16384
• Rémy Sigrist, Scatterplot of the first 2^16 terms

Crossrefs

See A328177 and A328178 for similar sequences.

Cf. A327987, A327988.

Programs

Maple

a:= n-> max(map(d-> Bits[And](d, n/d), numtheory[divisors](n))):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 09 2019

PARI

a(n) = vecmax(apply(d -> bitand(d, n/d), divisors(n)))

Formula

a(n)^2 <= n with equality iff n is a square.

a(n) = 1 for any odd prime number p.

a(n) <= A327987(n).

a(n) = 0 iff n belongs to A327988.