A305709 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.