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%I #9 Oct 03 2015 23:07:12
%S 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,
%T 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,
%U 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
%N a(n) = the number of positive divisors k of 2n where |k -2n/k| divides 2n.
%C For every odd positive integer n, |k - n/k| divides n for 0 divisors of n.
%e 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.
%p 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
%K nonn
%O 1,1
%A _Leroy Quet_, May 01 2008
%E More terms from _R. J. Mathar_, May 22 2008
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