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A305709 Least k such that there exists a three-term sequence n = b_1 < b_2 < b_3 = k such that b_1 * b_2 * b_3 is square.

%I A305709 #19 Jul 17 2018 16:07:04
%S A305709 8,6,8,16,10,12,14,18,25,20,22,20,26,24,27,32,34,27,38,30,28,33,46,32,
%T A305709 48,52,40,45,58,42,62,45,48,54,56,64,74,57,52,50,82,56,86,55,60,69,94,
%U A305709 54,72,63,75,78,106,75,90,72,76,96,118,80,122,96,84,98,104
%N A305709 Least k such that there exists a three-term sequence n = b_1 < b_2 < b_3 = k such that b_1 * b_2 * b_3 is square.
%C A305709 a(n) >= A006255(n), and a(n) = A006255(n) if and only if A066400(n) = 3.
%C A305709 Conjecture: a(n) < A072905(n) with finitely many nonsquare exceptions.
%H A305709 Peter Kagey, <a href="/A305709/b305709.txt">Table of n, a(n) for n = 1..10000</a>
%e A305709 For n = 3 the sequence is 3, 6, 8; so a(3) = 8;
%e A305709 for n = 4 the sequence is 4, 9, 16; so a(4) = 16;
%e A305709 for n = 5 the sequence is 5, 8, 10; so a(5) = 10.
%Y A305709 Cf. A006255, A066400, A072905.
%K A305709 nonn
%O A305709 1,1
%A A305709 _Peter Kagey_, Jun 08 2018