

A161840


Number of noncentral 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
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OFFSET

1,4


COMMENTS

Noncentral 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 noncentral 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 noncentral 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



