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

1,4

Links

Rémy Sigrist, Table of n, a(n) for n = 1..16384

Rémy Sigrist, Scatterplot of the first 2^16 terms

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.

Example

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.

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

Prog

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

Crossrefs

See A328177 and A328178 for similar sequences.

Cf. A327987, A327988.

Sequence in context: A030205 A159817 A079532 * A191312 A240159 A309447

Adjacent sequences: A328173 A328174 A328175 * A328177 A328178 A328179

Keyword

nonn,base

Author

Rémy Sigrist, Oct 06 2019

Status

approved