%I #12 Sep 07 2017 21:24:51
%S 2,4,6,6,6,10,6,8,10,10,6,14,6,10,14,10,6,16,6,14,14,10,6,18,10,10,14,
%T 14,6,22,6,12,14,10,14,22,6,10,14,18,6,22,6,14,22,10,6,22,10,16,14,14,
%U 6,22,14,18,14,10,6,30,6,10,22,14,14,22,6,14,14,22,6,28,6,10,22,14,14,22
%N a(n) is the number of integers of the form (n+k)/|(n-k)| for k>0.
%C a(n) <= 2^(n-1) and a(p)=6 for odd primes. - _Robert G. Wilson v_
%H Ivan Neretin, <a href="/A111150/b111150.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 2*tau(2n) - 2, tau = A000005. - _Ivan Neretin_, Sep 07 2017
%e For n=7 we have integer value for the form when k={5; 6; 8; 9; 14; 21} and (7+k)/|(7-k)| = {6, 13, 15, 8, 3, 2}. Thus a(7) = 6.
%t f[n_] := Length[ Select[(n + #)/Abs[n - # ] & /@ Delete[ Range[ Floor[5n/3]], n], IntegerQ[ # ] &]] + 2; Array[f, 78] (* _Robert G. Wilson v_ *)
%t Table[2 DivisorSigma[0, 2 n] - 2, {n, 78}] (* _Ivan Neretin_, Sep 07 2017 *)
%Y Cf. A000005.
%K easy,nonn
%O 1,1
%A _Paolo P. Lava_ & _Giorgio Balzarotti_, Oct 19 2005
%E Edited and extended by _Robert G. Wilson v_, Oct 19 2005