

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.


3



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
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OFFSET

1,2


LINKS



FORMULA

a(n)^2 >= n with equality iff n is a square.
a(p) = p for any odd prime number p.


EXAMPLE

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.


MAPLE

a:= n> min(map(d> Bits[Or](d, n/d), numtheory[divisors](n))):


PROG

(PARI) a(n) = vecmin(apply(d > bitor(d, n/d), divisors(n)))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



