%I #21 Mar 02 2019 12:06:58
%S 1,1,3,2,5,2,7,2,3,5,11,3,13,7,3,4,17,3,19,4,3,11,23,3,5,13,9,4,29,5,
%T 31,4,11,17,5,4,37,19,13,4,41,6,43,4,5,23,47,4,7,5,17,4,53,6,5,4,19,
%U 29,59,4,61,31,7,4,5,6,67,17,23,5,71,6,73,37,5,19,7,6,79,5,9,41,83,6,5,43,29,8,89,5,7,23,31,47,5,6,97,7,9,5,101,6,103,8,5,53
%N Shortest possible antipower period of a binary string of length n.
%C An antiperiod of a length-n string x is a divisor d of n such that if you factor x as the concatenation of (n/d) blocks of length d, then all these blocks are distinct.
%C k*2^k (A036289(k)) is the largest number n that makes a(n) = k. - _Jinyuan Wang_, Feb 15 2019
%H Jinyuan Wang, <a href="/A274457/b274457.txt">Table of n, a(n) for n = 1..10000</a>
%H G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, <a href="http://arxiv.org/abs/1606.02868">Anti-powers in infinite words</a>, arxiv preprint, 1606.02868v1 [cs.DM], June 9 2016.
%F a(n) is the smallest divisor d of n such that n/d <= 2^d.
%t a[n_] := Do[If[n/d <= 2^d, Return[d]], {d, Divisors[n]}];
%t Array[a, 106] (* _Jean-François Alcover_, Feb 15 2019 *)
%o (PARI) a(n) = fordiv(n, d, if (n/d <= 2^d, return (d))); \\ _Michel Marcus_, Feb 15 2019
%Y Cf. A036289, A274409, A274449, A274450, A274451.
%K nonn
%O 1,3
%A _Jeffrey Shallit_, Jun 23 2016