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A158977
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Product of the numbers k in the range 1 <= k <= n such that the proper divisors of k are a subset of the proper divisors of n.
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0
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1, 2, 6, 24, 30, 720, 210, 6720, 1890, 8400, 2310, 47900160, 30030, 1681680, 4054050, 15375360, 510510, 1984862880, 9699690, 62078016000, 1833241410, 853572720, 223092870, 1776404640890880, 5577321750, 23201658480, 54211567410
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OFFSET
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1,2
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COMMENTS
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Here, proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as counted in A032741.
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LINKS
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FORMULA
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EXAMPLE
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a(8) = 6720 is the product of the 7 numbers k: 1 {1}, 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with divisor set that are subsets of {1, 2, 4} for n = 8. 1 * 2 * 3 * 4 * 5 * 7 * 8 = 6720.
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PROG
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(Magma) [ &*[ k: k in [1..n] | forall(t){ d: d in Divisors(k) | d eq k or d in Divisors(n) } ]: n in [1..27] ]; // Klaus Brockhaus, Apr 07 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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