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A161840
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Number of non-central divisors of n.
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4
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0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 4, 0, 2, 2, 4, 0, 4, 0, 4, 2, 2, 0, 6, 2, 2, 2, 4, 0, 6, 0, 4, 2, 2, 2, 8, 0, 2, 2, 6, 0, 6, 0, 4, 4, 2, 0, 8, 2, 4, 2, 4, 0, 6, 2, 6, 2, 2, 0, 10, 0, 2, 4, 6, 2, 6, 0, 4, 2, 6, 0, 10, 0, 2, 4, 4, 2, 6, 0, 8, 4, 2, 0, 10, 2, 2, 2, 6, 0, 10, 2, 4, 2, 2, 2, 10, 0, 4, 4, 8
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OFFSET
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1,4
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COMMENTS
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Non-central divisors in the following sense: if we sort the divisors of n in natural order, there is one "central", median divisor if the number of divisors tau(n) = A000005(n) is odd, and there are two "central" divisors if tau(n) is even. a(n) is the number of divisors not counting the median or two central divisors.
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LINKS
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Table of n, a(n) for n=1..100.
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FORMULA
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a(n) = tau(n)-2 + (tau(n) mod 2), tau = A000005.
a(n) = A000005(n) - A049240(n) - 1.
a(n) = A000005(n) + A010052(n) - 2.
a(n) = A000005(n) - A169695(n).
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EXAMPLE
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The divisors of 4 are 1, 2, 4 so the non-central divisors of 4 are 1, 4 because its central divisor is 2.
The divisors of 12 are 1, 2, 3, 4, 6, 12 so the non-central divisors of 12 are 1, 2, 6, 12 because its central divisors are 3, 4.
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MAPLE
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A000005 := proc(n) numtheory[tau](n) ; end: A010052 := proc(n) if issqr(n) then 1; else 0 ; fi; end: A161840 := proc(n) A000005(n)+A010052(n)-2 ; end: seq(A161840(n), n=1..100) ; [From R. J. Mathar, Jul 04 2009]
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CROSSREFS
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Cf. A000005, A049240, A010052, A161841, A169695, A183002, A183003.
Sequence in context: A204173 A103668 A076472 * A140302 A085341 A221474
Adjacent sequences: A161837 A161838 A161839 * A161841 A161842 A161843
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, Jun 21 2009
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EXTENSIONS
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More terms from R. J. Mathar, Jul 04 2009
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STATUS
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approved
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