%I A073772
%S A073772 0,0,1,0,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,2,2,1,1,1,1,1,2,1,2,2,1,
%T A073772 1,1,1,1,1,2,1,2,2,1,2,2,2,1,1,2,1,2,1,2,2,1,2,2,2,1,1,2,2,2,1,2,3,1,1,
%U A073772 2,2,2,1,1,1,1,1,1,1,1,3,3,3,3,1,1,2,2,2,1,1,1,1,3,3,3,3
%V A073772 0,0,-1,0,0,1,-1,-1,0,1,1,-1,0,-1,1,1,-1,0,1,1,1,-1,-1,2,2,-1,-1,1,1,1,
               2,-1,2,2,-1,-1,
%W A073772 -1,1,1,1,2,-1,2,2,-1,2,2,2,-1,-1,2,-1,2,-1,2,2,-1,2,2,2,-1,-1,2,2,2,-1,
               2,3,-1,-1,2,2,
%X A073772 2,-1,-1,1,1,1,1,-1,-1,3,3,3,3,-1,-1,2,2,2,-1,1,1,-1,3,3,3,3
%N A073772 Number of highly composite numbers (HCNs) between the n-th highly composite 
               number k and 2*k if 2*k is a highly composite number, or -1 if 2*k 
               is not a highly composite number.
%C A073772 If 2*A002182(n) = A002182(m) then a(n) = m - n - 1; if 2*A002182(n) is 
               not a highly composite number then a(n) = -1. The zero terms correspond 
               to the terms of A072938, the negative terms correspond to the terms 
               of A073771. The terms were determined by means of A. Flammenkamp's 
               list (cf. Links).
%H A073772 Achim Flammenkamp <a href="http://www.uni-bielefeld.de/~achim/highly.html">
               Highly Composite Numbers</a>
%e A073772 a(3) = -1 since 4 is the third highly composite number and 2*4 = 8 is 
               not a highly composite number; a(6) = 1 since 24 is the sixth highly 
               composite number, 2*24 = 48 is the eighth highly composite number 
               and the highly composite number 36 is between them; a(13) = 0 since 
               360 is the 13th highly composite number, 2*360 = 720 is the 14th 
               highly composite number and there is no highly composite number between 
               them.
%Y A073772 Cf. A002182, A072938, A073771.
%Y A073772 Sequence in context: A099564 A126389 A105551 this_sequence A164562 A058188 
               A070000
%Y A073772 Adjacent sequences: A073769 A073770 A073771 this_sequence A073773 A073774 
               A073775
%K A073772 sign
%O A073772 1,24
%A A073772 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 19 2002