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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.

%I A300516 #9 Mar 18 2018 09:56:19
%S A300516 1,4,9,4,25,12,49,16,9,25,121,18,169,49,25,16,289,25,361,25,49,121,
%T A300516 529,48,25,169,81,49,841,50,961,64,121,289,50,36,1369
%N 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.
%C A300516 For all n, a(n^2) = n^2, and for all prime p, a(p) = p^2.
%C A300516 a(n) is bounded below by max(n, A006530(A007913(n))^2) and above by n^2.
%e A300516 Some valid sequences for n = 2, 4, 6, 12, 15, and 24 are
%e A300516 a(2) = 4   via lcm(2, 4)           = 2^2,
%e A300516 a(4) = 4   via lcm(4)              = 2^2,
%e A300516 a(6) = 12  via lcm(6, 9, 12)       = 12^2,
%e A300516 a(12) = 18 via lcm(12, 18)         = 6^2,
%e A300516 a(15) = 25 via lcm(15, 16, 18, 25) = 60^2, and
%e A300516 a(24) = 48 via lcm(24, 36, 48)     = 12^2.
%Y A300516 Cf. A006255, A277278.
%K A300516 nonn,more
%O A300516 1,2
%A A300516 _Peter Kagey_, Mar 07 2018