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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. 1

%I

%S 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 48,52,40,45,58,42,62,45,48,54,56,64,74,57,52,50,82,56,86,55,60,69,94,

%U 54,72,63,75,78,106,75,90,72,76,96,118,80,122,96,84,98,104

%N 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 a(n) >= A006255(n), and a(n) = A006255(n) if and only if A066400(n) = 3.

%C Conjecture: a(n) < A072905(n) with finitely many nonsquare exceptions.

%H Peter Kagey, <a href="/A305709/b305709.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 3 the sequence is 3, 6, 8; so a(3) = 8;

%e for n = 4 the sequence is 4, 9, 16; so a(4) = 16;

%e for n = 5 the sequence is 5, 8, 10; so a(5) = 10.

%Y Cf. A006255, A066400, A072905.

%K nonn

%O 1,1

%A _Peter Kagey_, Jun 08 2018

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Last modified March 29 01:21 EDT 2023. Contains 361596 sequences. (Running on oeis4.)