%I A136180
%S A136180 0,1,1,3,1,5,1,7,4,7,1,11,1,9,7,15,1,17,1,19,9,13,1,23,6,15,13,25,1,26,
%T A136180 1,31,13,19,9,35,1,21,15,37,1,41,1,37,21,25,1,47,8,37,19,43,1,53,13,49,
%U A136180 21,31,1,57,1,33,27,63,15,61,1,55,25,48
%N A136180 a(n) = sum{k=1 to d(n)-1) GCD(b(k),b(k+1)), where b(k) is the kth positive 
               divisor of n and d(n) = the number of positive divisors of n.
%C A136180 a(n) = the sum of the terms in row n of A136178.
%H A136180 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A136180 The positive divisors of 20 are 1,2,4,5,10,20. GCD(1,2)=1. GCD(2,4)=2. 
               GCD(4,5)=1. GCD(5,10)=5. And GCD(10,20)=10. So a(20) = 1+2+1+5+10 
               = 19.
%p A136180 with(numtheory): a:=proc(n) local div: div:=divisors(n): add(gcd(div[k], 
               div[k+1]),k=1..tau(n)-1) end proc: seq(a(n),n=1..70); - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Jan 08 2008
%Y A136180 Cf. A136178, A136179, A136183.
%Y A136180 Sequence in context: A147088 A118402 A122383 this_sequence A095112 A160596 
               A092319
%Y A136180 Adjacent sequences: A136177 A136178 A136179 this_sequence A136181 A136182 
               A136183
%K A136180 more,nonn
%O A136180 1,4
%A A136180 Leroy Quet Dec 19 2007
%E A136180 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 08 2008