

A303297


List of middle divisors: for every positive integer that has middle divisors, add its middle divisors to the sequence.


8



1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 5, 4, 3, 4, 5, 4, 6, 5, 4, 7, 5, 6, 4, 5, 7, 6, 5, 8, 6, 7, 5, 9, 6, 8, 7, 5, 6, 9, 7, 8, 6, 10, 7, 9, 8, 6, 11, 7, 10, 6, 8, 9, 7, 11, 8, 10, 9, 7, 12, 8, 11, 9, 10, 7, 13, 8, 12, 7, 9, 11, 10, 8, 13, 9, 12, 10, 11, 8, 14, 9, 13, 8, 10, 12, 15, 11, 9, 14, 8, 10, 13, 11, 12, 9, 15
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OFFSET

1,3


COMMENTS

The middle divisors of k (see A299761) are the divisors in the halfopen interval [sqrt(k/2), sqrt(k*2)), k >= 1.


LINKS

Table of n, a(n) for n=1..95.


EXAMPLE

The middle divisor of 1 is 1, so a(1) = 1.
The middle divisor of 2 is 1, so a(2) = 1.
There are no middle divisors of 3.
The middle divisor of 4 is 2, so a(3) = 2.
There are no middle divisors of 5.
The middle divisors of 6 are 2 and 3, so a(4) = 2 and a(5) = 3.
There are no middle divisors of 7.
The middle divisor of 8 is 2, so a(6) = 2.
The middle divisor of 9 is 3, so a(7) = 3.
There are no middle divisors of 10.
There are no middle divisors of 11.
The middle divisors of 12 are 3 and 4, so a(8) = 3 and a(9) = 4.


MATHEMATICA

Table[Select[Divisors@ n, Sqrt[n/2] <= # < Sqrt[2 n] &] /. {} > Nothing, {n, 135}] // Flatten (* Michael De Vlieger, Jun 14 2018 *)


CROSSREFS

Concatenate the nonzero rows of A299761 (that is, the nonzero terms of A299761).
Cf. A027750, A067742, A071090, A071562, A281007, A299777.
Sequence in context: A277329 A071330 A092333 * A107452 A205018 A286716
Adjacent sequences: A303294 A303295 A303296 * A303298 A303299 A303300


KEYWORD

nonn


AUTHOR

Omar E. Pol, Apr 30 2018


STATUS

approved



