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%I #21 Mar 04 2018 17:45:10
%S 0,2,3,6,5,14,7,14,12,22,11,44,13,30,33,30,17,50,19,56,45,46,23,104,
%T 30,54,39,76,29,143,31,62,69,70,75,158,37,78,81,166,41,154,43,116,153,
%U 94,47,224,56,122,105,136,53,158,115,230,117,118,59,400,61,126,213,126,135
%N a(n) = Sum_{k=1..d(n)-1} lcm(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) = number of positive divisors of n.
%C a(n) = sum of the terms in row n of A136181.
%H H. v. Eitzen, <a href="/A136183/b136183.txt">Table of n, a(n) for n=1..10000</a>
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%e The positive divisors of 20 are 1,2,4,5,10,20; lcm(1,2)=2, lcm(2,4)=4, lcm(4,5)=20, lcm(5,10)=10, and lcm(10,20)=20, so a(20) = 2+4+20+10+20 = 56.
%p A136181row := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n),list)) ; seq(lcm(op(d-1,dvs),op(d,dvs)),d=2..nops(dvs)) ; end: A136183 := proc(n) if n = 1 then 0; else add(l,l= A136181row(n) ) ; fi; end: seq(A136183 (n),n=1..70) ; # _R. J. Mathar_, Jul 20 2009
%t Table[Total@ Apply[LCM, Partition[Divisors@ n, 2, 1], 1], {n, 65}] (* _Michael De Vlieger_, Sep 21 2017 *)
%o (PARI) A136183(n) = local(d=divisors(n)); vector(#d-1,x,lcm(d[x],d[x+1]))*vector(#d-1,x,1)~
%o (PARI) a(n) = my(d=divisors(n)); vecsum(vector(#d-1, k, lcm(d[k], d[k+1]))); \\ _Michel Marcus_, Sep 22 2017
%o (Haskell)
%o a136183 n = sum $ zipWith lcm ps $ tail ps where ps = a027750_row n
%o -- _Reinhard Zumkeller_, Dec 20 2014
%Y Cf. A136180, A136181, A136182.
%Y Cf. A027750.
%K nonn
%O 1,2
%A _Leroy Quet_, Dec 19 2007
%E Extended beyond a(12) by _R. J. Mathar_, Jul 20 2009
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