A328177 a(n) is the minimal value of the expression d OR (n/d) where d runs through the divisors of n and OR denotes the bitwise OR operator.
1, 3, 3, 2, 5, 3, 7, 6, 3, 7, 11, 6, 13, 7, 7, 4, 17, 7, 19, 5, 7, 11, 23, 6, 5, 15, 11, 7, 29, 7, 31, 12, 11, 19, 7, 6, 37, 19, 15, 13, 41, 7, 43, 15, 13, 23, 47, 12, 7, 15, 19, 13, 53, 15, 15, 14, 19, 31, 59, 13, 61, 31, 15, 8, 13, 15, 67, 21, 23, 15, 71, 9
Offset: 1
Examples
For n = 12:
- we have the following values:
d 12/d d OR (12/d)
-- ---- -----------
1 12 13
2 6 6
3 4 7
4 3 7
6 2 6
12 1 13
- hence a(12) = min({6, 7, 13}) = 6.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..16384
- Rémy Sigrist, Logarithmic scatterplot of the first 2^16 terms
Programs
-
Maple
a:= n-> min(map(d-> Bits[Or](d, n/d), numtheory[divisors](n))): seq(a(n), n=1..100); # Alois P. Heinz, Oct 09 2019
-
PARI
a(n) = vecmin(apply(d -> bitor(d, n/d), divisors(n)))
Formula
a(n)^2 >= n with equality iff n is a square.
a(p) = p for any odd prime number p.