A138021 a(n) = the number of positive divisors k of 2n where |k -2n/k| divides 2n.

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

Offset

1,1

Comments

For every odd positive integer n, |k - n/k| divides n for 0 divisors of n.

Links

Table of n, a(n) for n=1..105.

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

Adjacent sequences: A138018 A138019 A138020 * A138022 A138023 A138024

Keyword

nonn

Author

Leroy Quet, May 01 2008

Extensions

More terms from R. J. Mathar, May 22 2008

Status

approved