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Search: id:A069023
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| A069023 |
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Define a subset of divisors of n to be a dedicated subset if the product of any two members is also a divisor of n. 1 is not allowed as a member as it gives trivially 1*d = d a divisor. a(n) is the number of dedicated subsets of divisors of n with at least two members. |
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| 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 1, 2, 0, 3, 0, 3, 1, 1, 0, 9, 0, 1, 1, 3, 0, 7, 0, 5, 1, 1, 1, 9, 0, 1, 1, 9, 0, 7, 0, 3, 3, 1, 0, 17, 0, 3, 1, 3, 0, 9, 1, 9, 1, 1, 0, 20, 0, 1, 3, 8, 1, 7, 0, 3, 1, 7, 0, 28, 0, 1, 3, 3, 1, 7, 0, 17, 2, 1, 0, 20, 1, 1, 1, 9, 0, 20, 1, 3, 1, 1, 1, 35, 0, 3, 3, 9, 0, 7
(list; graph; listen)
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OFFSET
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1,12
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COMMENT
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a(n) is determined by the prime signature of n.
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EXAMPLE
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a(12) = 3. The divisors of 12 are 1,2,3,4,6,12. The divisor subsets (2,3),(2,6) and (3,4) are such that their product is also a divisor of 12. a(24) = 9 and the dedicated divisor subsets are (2,3),(2,4),(2,6),(2,12),(3,4),(3,8),(4,6),(2,3,4),(2,4,6).
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CROSSREFS
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Sequence in context: A048838 A059341 A131802 this_sequence A091614 A029358 A088512
Adjacent sequences: A069020 A069021 A069022 this_sequence A069024 A069025 A069026
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 02 2002
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EXTENSIONS
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Edited by David Wasserman (wasserma(AT)spawar.navy.mil), Mar 26 2003
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