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A300516
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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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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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