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

1,2

Links

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

Rémy Sigrist, Logarithmic scatterplot of the first 2^16 terms

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))):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 09 2019

Prog

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

Crossrefs

See A328176 and A328178 for similar sequences.

Cf. A218388.

Sequence in context: A110897 A116644 A166462 * A320776 A279056 A265751

Adjacent sequences: A328174 A328175 A328176 * A328178 A328179 A328180

Keyword

nonn,base

Author

Rémy Sigrist, Oct 06 2019

Status

approved