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A260842 Sum of lcm(gcd(i,j), gcd(k,l)) for i,j,k,l in range [1..n].

%I A260842 #28 Mar 02 2019 04:21:08
%S A260842 1,23,136,516,1289,3271,5908,11084,18833,31503,44072,71156,93681,
%T A260842 133095,190052,256468,311909,421619,501412,664112,847013,1035763,
%U A260842 1186208,1515000,1790625,2114575,2502268,3028600,3354613,4109163,4517824,5246624,6070201,6853807,7933304
%N A260842 Sum of lcm(gcd(i,j), gcd(k,l)) for i,j,k,l in range [1..n].
%H A260842 Giovanni Resta, <a href="/A260842/b260842.txt">Table of n, a(n) for n = 1..10000</a> (first 161 terms from Robert G. Wilson v)
%H A260842 Ren LuYao (FancyCoder), <a href="http://acm.hdu.edu.cn/showproblem.php?pid=5341">Round #49</a>, BestCoder.
%p A260842 N:= 100: # to get a(1) to a(N)
%p A260842 M:= Matrix(N,N,igcd,shape=symmetric):
%p A260842 T:= Vector(N):
%p A260842 for n from 1 to N do
%p A260842   T[M[n,n]]:= T[M[n,n]]+1;
%p A260842   for j from 1 to n-1 do
%p A260842     T[M[n,j]]:= T[M[n,j]]+2;
%p A260842   od:
%p A260842   A[n]:= 2*add(add(ilcm(i,j)*T[i]*T[j],i=1..j-1),j=2..n) + add(i*T[i]^2,i=1..n);
%p A260842 od:
%p A260842 seq(A[n],n=1..N); # _Robert Israel_, Aug 04 2015
%t A260842 f[n_] := Sum[ LCM[ GCD[i, j], GCD[k, l]], {i, n}, {j, n}, {k, n}, {l, n}]; Array[f, 35] (* _Robert G. Wilson v_, Aug 02 2015 *)
%o A260842 (PARI) a(n) = {s = 0; for (i=1, n, for (j=1, n, for (k=1, n, for (l=1, n, s += lcm(gcd(i,j),gcd(k,l)););););); s;} \\ _Michel Marcus_, Aug 01 2015
%K A260842 nonn
%O A260842 1,2
%A A260842 _Sirius Caffrey_, Aug 01 2015
%E A260842 More terms from _Michel Marcus_, Aug 01 2015