A328177 -id:A328177 - cp's OEIS frontend

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

Rémy Sigrist, Oct 06 2019

			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.

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

See A328177 and A328178 for similar sequences.

Cf. A327987, A327988.

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

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

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.

A328178 a(n) is the minimal value of the expression d XOR (n/d) where d runs through the divisors of n and XOR denotes the bitwise XOR operator.

Original entry on oeis.org

0, 3, 2, 0, 4, 1, 6, 6, 0, 7, 10, 4, 12, 5, 6, 0, 16, 5, 18, 1, 4, 9, 22, 2, 0, 15, 10, 3, 28, 3, 30, 12, 8, 19, 2, 0, 36, 17, 14, 13, 40, 1, 42, 15, 12, 21, 46, 8, 0, 15, 18, 9, 52, 15, 14, 10, 16, 31, 58, 9, 60, 29, 14, 0, 8, 13, 66, 21, 20, 11, 70, 1, 72

Offset: 1

Rémy Sigrist, Oct 06 2019

			For n = 12:
- we have the following values:
    d   12/d  d XOR (12/d)
    --  ----  ------------
     1    12            13
     2     6             4
     3     4             7
     4     3             7
     6     2             4
    12     1            13
- hence a(12) = min({4, 7, 13}) = 4.

Rémy Sigrist, Table of n, a(n) for n = 1..16384
Rémy Sigrist, Logarithmic scatterplot of (n, 1+a(n)) for n = 1..2^16

See A328176 and A328177 for similar sequences.

Cf. A178910.

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

mvx[n_]:=Min[BitXor[#,n/#]&/@Divisors[n]]; Array[mvx,80] (* Harvey P. Dale, Nov 04 2019 *)

a(n) = vecmin(apply(d -> bitxor(d, n/d), divisors(n)))

a(n) = 0 iff n is a square.

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

cp's OEIS Frontend

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.

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