A328176 - OEIS

%I #19 Oct 12 2019 08:34:11

%S 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,

%T 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,

%U 3,4,1,8,1,0,5,2,3,4,1,8,9,0,1,6,1,2,1

%N 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.

%H Rémy Sigrist, <a href="/A328176/b328176.txt">Table of n, a(n) for n = 1..16384</a>

%H Rémy Sigrist, <a href="/A328176/a328176.png">Scatterplot of the first 2^16 terms</a>

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

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

%F a(n) <= A327987(n).

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

%e For n = 12:

%e - we have the following values:

%e     d   12/d  d AND (12/d)

%e     --  ----  ------------

%e      1    12             0

%e      2     6             2

%e      3     4             0

%e      4     3             0

%e      6     2             2

%e     12     1             0

%e - hence a(12) = max({0, 2}) = 2.

%p a:= n-> max(map(d-> Bits[And](d, n/d), numtheory[divisors](n))):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 09 2019

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

%Y See A328177 and A328178 for similar sequences.

%Y Cf. A327987, A327988.

%K nonn,base

%O 1,4

%A _Rémy Sigrist_, Oct 06 2019