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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.
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%I #9 Mar 18 2018 09:56:19

%S 1,4,9,4,25,12,49,16,9,25,121,18,169,49,25,16,289,25,361,25,49,121,

%T 529,48,25,169,81,49,841,50,961,64,121,289,50,36,1369

%N 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.

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

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

%e Some valid sequences for n = 2, 4, 6, 12, 15, and 24 are

%e a(2) = 4 via lcm(2, 4) = 2^2,

%e a(4) = 4 via lcm(4) = 2^2,

%e a(6) = 12 via lcm(6, 9, 12) = 12^2,

%e a(12) = 18 via lcm(12, 18) = 6^2,

%e a(15) = 25 via lcm(15, 16, 18, 25) = 60^2, and

%e a(24) = 48 via lcm(24, 36, 48) = 12^2.

%Y Cf. A006255, A277278.

%K nonn,more

%O 1,2

%A _Peter Kagey_, Mar 07 2018