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A138021 a(n) = the number of positive divisors k of 2n where |k -2n/k| divides 2n. 1
2, 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For every odd positive integer n, |k - n/k| divides n for 0 divisors of n.
LINKS
EXAMPLE
The positive divisors of 12 are 1,2,3,4,6,12. Checking: |1- 12/1|=11 does not divide 12. |2- 12/2|=4 does divide 12. |3- 12/3|=1 does divide 12. |4- 12/4|=1 does divide 12. |6- 12/6|=4 does divide 12. And |12- 12/12|=11 does not divide 12. There are therefore four divisors k of 12 where |k -12/k| divides 12. So a(6) = 4.
MAPLE
A138021 := proc(n) local a, k ; a := 0 ; for k in numtheory[divisors](2*n) do if k-2*n/k <> 0 then if (2*n) mod abs(k-2*n/k) = 0 then a := a+1 ; fi ; fi ; od: a; end: seq(A138021(n), n=1..120) ; # R. J. Mathar, May 22 2008
CROSSREFS
Sequence in context: A346274 A214258 A369279 * A166065 A252706 A139137
KEYWORD
nonn
AUTHOR
Leroy Quet, May 01 2008
EXTENSIONS
More terms from R. J. Mathar, May 22 2008
STATUS
approved

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Last modified May 28 12:54 EDT 2024. Contains 372913 sequences. (Running on oeis4.)