

A305709


Least k such that there exists a threeterm sequence n = b_1 < b_2 < b_3 = k such that b_1 * b_2 * b_3 is square.


1



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.


CROSSREFS

Cf. A006255, A066400, A072905.
Sequence in context: A246768 A088541 A110214 * A093721 A091506 A021539
Adjacent sequences: A305706 A305707 A305708 * A305710 A305711 A305712


KEYWORD

nonn


AUTHOR

Peter Kagey, Jun 08 2018


STATUS

approved



