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A161840 Number of non-central divisors of n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

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).

EXAMPLE

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.

MAPLE

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]

CROSSREFS

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

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Jun 21 2009

EXTENSIONS

More terms from R. J. Mathar, Jul 04 2009

STATUS

approved

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Last modified July 23 23:07 EDT 2014. Contains 244873 sequences.