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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.

%I A328177 #13 Oct 09 2019 10:56:35
%S A328177 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 A328177 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 A328177 15,14,19,31,59,13,61,31,15,8,13,15,67,21,23,15,71,9
%N 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.
%H A328177 Rémy Sigrist, <a href="/A328177/b328177.txt">Table of n, a(n) for n = 1..16384</a>
%H A328177 Rémy Sigrist, <a href="/A328177/a328177.png">Logarithmic scatterplot of the first 2^16 terms</a>
%F A328177 a(n)^2 >= n with equality iff n is a square.
%F A328177 a(p) = p for any odd prime number p.
%e A328177 For n = 12:
%e A328177 - we have the following values:
%e A328177     d   12/d  d OR (12/d)
%e A328177     --  ----  -----------
%e A328177      1    12           13
%e A328177      2     6            6
%e A328177      3     4            7
%e A328177      4     3            7
%e A328177      6     2            6
%e A328177     12     1           13
%e A328177 - hence a(12) = min({6, 7, 13}) = 6.
%p A328177 a:= n-> min(map(d-> Bits[Or](d, n/d), numtheory[divisors](n))):
%p A328177 seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 09 2019
%o A328177 (PARI) a(n) = vecmin(apply(d -> bitor(d, n/d), divisors(n)))
%Y A328177 See A328176 and A328178 for similar sequences.
%Y A328177 Cf. A218388.
%K A328177 nonn,base
%O A328177 1,2
%A A328177 _Rémy Sigrist_, Oct 06 2019