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.

8, 6, 8, 16, 10, 12, 14, 18, 25, 20, 22, 20, 26, 24, 27, 32, 34, 27, 38, 30, 28, 33, 46, 32, 48, 52, 40, 45, 58, 42, 62, 45, 48, 54, 56, 64, 74, 57, 52, 50, 82, 56, 86, 55, 60, 69, 94, 54, 72, 63, 75, 78, 106, 75, 90, 72, 76, 96, 118, 80, 122, 96, 84, 98, 104

Offset: 1

Author

Peter Kagey, Jun 08 2018

Keywords

• nonn

Comments

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

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

Examples

			For n = 3 the sequence is 3, 6, 8; so a(3) = 8;
for n = 4 the sequence is 4, 9, 16; so a(4) = 16;
for n = 5 the sequence is 5, 8, 10; so a(5) = 10.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006255, A066400, A072905.