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A181825
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Members of A025487 whose prime signature is self-conjugate (as a partition).
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10
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1, 2, 12, 36, 120, 360, 1680, 5040, 5400, 27000, 36960, 75600, 110880, 378000, 960960, 1587600, 1663200, 2882880, 7938000, 8316000, 32672640, 34927200, 43243200, 98017920, 174636000, 216216000, 277830000, 908107200, 1152597600, 1241560320, 1470268800, 1944810000
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OFFSET
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1,2
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COMMENTS
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Closed under the binary operations of GCD and LCM, since a self-conjugate partition of Omega(a(n)) (which the prime signature of these numbers is) is the concatenation of self-conjugate hooks of decreasing size while moving downward and to the right in the Ferrers diagram, and the GCD (or LCM) of two terms a(i) and a(j) is obtained by taking the smaller (or larger, respectively) of the corresponding hooks. For example, GCD(a(8),a(11)) = GCD(5040,36960) = 1680 = a(7), and LCM(a(8),a(11)) = 110880 = a(13). The two binary operations make the set {a(n)} into a lattice order. - Richard Peterson, May 29 2020
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LINKS
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EXAMPLE
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A025487(11) = 36 = 2^2*3^2 has a prime signature of (2,2), which is a self-conjugate partition; hence, 36 is included in the sequence.
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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