%I A055081
%S A055081 1,2,3,3,3,7,3,4,5,6,3,10,3,6,10,5,3,11,3,10,9,6,3,13,5,6,7,10,3,20,3,
%T A055081 6,9,6,10,16,3,6,9,13,3,20,3,9,17,6,3,16,5,10,9,9,3,15,9,13,9,6,3,30,3,
%U A055081 6,16,7,9,20,3,9,9,19,3,22,3,6,16,9,10,19,3,16,9,6,3,30,9,6,9,13,3,33
%N A055081 Number of positive integers whose harmonic mean with n is a positive 
               integer.
%C A055081 Also the number of factors of 2n^2 which are less than 2n, since the 
               harmonic mean of n and 2n^2/k-n is 2n-k and these are all positive 
               integers iff k<2n is a factor of 2n^2. So a(n)=3 iff n=4 or n is 
               an odd prime.
%e A055081 a(6)=7 since the pairwise harmonic means of 6 with 2, 3, 6, 12, 18, 30 
               and 66 are 3, 4, 6, 8, 9, 10 and 11 respectively.
%Y A055081 The smallest and largest positive integers whose harmonic means with 
               n are positive integers are A053626 and A000384 with harmonic means 
               of A053627 and A004273.
%Y A055081 Sequence in context: A049982 A070167 A141479 this_sequence A109833 A132005 
               A088041
%Y A055081 Adjacent sequences: A055078 A055079 A055080 this_sequence A055082 A055083 
               A055084
%K A055081 nonn
%O A055081 1,2
%A A055081 Henry Bottomley (se16(AT)btinternet.com), Jun 13 2000