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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.
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%I #13 Oct 09 2019 10:56:35

%S 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,

%T 31,12,11,19,7,6,37,19,15,13,41,7,43,15,13,23,47,12,7,15,19,13,53,15,

%U 15,14,19,31,59,13,61,31,15,8,13,15,67,21,23,15,71,9

%N 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.

%H Rémy Sigrist, <a href="/A328177/b328177.txt">Table of n, a(n) for n = 1..16384</a>

%H Rémy Sigrist, <a href="/A328177/a328177.png">Logarithmic scatterplot of the first 2^16 terms</a>

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

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

%e For n = 12:

%e - we have the following values:

%e d 12/d d OR (12/d)

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

%e 1 12 13

%e 2 6 6

%e 3 4 7

%e 4 3 7

%e 6 2 6

%e 12 1 13

%e - hence a(12) = min({6, 7, 13}) = 6.

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

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

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

%Y See A328176 and A328178 for similar sequences.

%Y Cf. A218388.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Oct 06 2019