A300516 a(n) is the least k such that there exists a strictly increasing sequence n = b_1 < b_2 < ... < b_t = k where lcm(b_1, b_2, ..., b_t) is square.

1, 4, 9, 4, 25, 12, 49, 16, 9, 25, 121, 18, 169, 49, 25, 16, 289, 25, 361, 25, 49, 121, 529, 48, 25, 169, 81, 49, 841, 50, 961, 64, 121, 289, 50, 36, 1369

Offset: 1

Author

Peter Kagey, Mar 07 2018

Keywords

• nonn
• more

Comments

For all n, a(n^2) = n^2, and for all prime p, a(p) = p^2.

a(n) is bounded below by max(n, A006530(A007913(n))^2) and above by n^2.

Examples

			Some valid sequences for n = 2, 4, 6, 12, 15, and 24 are
a(2) = 4   via lcm(2, 4)           = 2^2,
a(4) = 4   via lcm(4)              = 2^2,
a(6) = 12  via lcm(6, 9, 12)       = 12^2,
a(12) = 18 via lcm(12, 18)         = 6^2,
a(15) = 25 via lcm(15, 16, 18, 25) = 60^2, and
a(24) = 48 via lcm(24, 36, 48)     = 12^2.
		

Crossrefs

Cf. A006255, A277278.