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Search: id:A132747
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| A132747 |
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a(n) = number of non-isolated divisors of n. |
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+0
8
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| 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 5, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 5, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 3, 0, 2, 0, 2, 0, 6, 0, 2, 0, 2, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 7, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 3, 0, 2, 0
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A divisor d of n is non-isolated if either d-1 or d+1 divides n. a(2n-1) = 0 for all n >= 1.
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LINKS
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Ray Chandler, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) = A000005(n) - A132881(n).
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EXAMPLE
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The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are next to each other, and 4 and 5 are next to each other. So a(20) = the number of these diviors, which is 4.
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MATHEMATICA
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Table[Length[Select[Divisors[n], If[ # > 1, IntegerQ[n/(#*(# - 1))]] || IntegerQ[n/(#*(# + 1))] &]], {n, 1, 90}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 26 2007
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CROSSREFS
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Cf. A129308, A132748.
Sequence in context: A097974 A139036 A090330 this_sequence A053399 A117773 A025805
Adjacent sequences: A132744 A132745 A132746 this_sequence A132748 A132749 A132750
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Aug 27 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 26 2007
Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 24 2008
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