

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
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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 k2*n/k <> 0 then if (2*n) mod abs(k2*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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



