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A182862
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Numbers n that set a record for the number of distinct prime signatures represented among its unitary divisors.
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5
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1, 2, 6, 12, 60, 360, 1260, 2520, 27720, 138600, 360360, 831600, 10810800
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OFFSET
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1,2
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COMMENTS
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In other words, the sequence includes n iff A182860(n) > A182860(m) for all m < n.
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LINKS
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Table of n, a(n) for n=1..13.
Eric Weisstein's World of Mathematics, Unitary Divisor
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EXAMPLE
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60 has 8 unitary divisors (1, 3, 4, 5, 12, 15, 20 and 60). Primes 3 and 5 have the same prime signature, as do 12 (2^2*3) and 20 (2^2*5); each of the other four numbers listed is the only unitary divisor of 60 with its particular prime signature. This makes a total of 6 distinct prime signatures that appear among the unitary divisors of 60. Since no positive integer smaller than 60 has more than 4 distinct prime signatures appearing among its unitary divisors, 60 belongs to this sequence.
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CROSSREFS
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Subsequence of A025487, A129912, A181826, A182863. See also A034444, A085082, A182860, A182861.
Sequence in context: A072489 A072487 A189394 * A072938 A160274 A048803
Adjacent sequences: A182859 A182860 A182861 * A182863 A182864 A182865
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KEYWORD
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nonn,more
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AUTHOR
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Matthew Vandermast, Jan 14 2011
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STATUS
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approved
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