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A260842
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Sum of lcm(gcd(i,j), gcd(k,l)) for i,j,k,l in range [1..n].
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1
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1, 23, 136, 516, 1289, 3271, 5908, 11084, 18833, 31503, 44072, 71156, 93681, 133095, 190052, 256468, 311909, 421619, 501412, 664112, 847013, 1035763, 1186208, 1515000, 1790625, 2114575, 2502268, 3028600, 3354613, 4109163, 4517824, 5246624, 6070201, 6853807, 7933304
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OFFSET
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1,2
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LINKS
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Ren LuYao (FancyCoder), Round #49, BestCoder.
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MAPLE
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N:= 100: # to get a(1) to a(N)
M:= Matrix(N, N, igcd, shape=symmetric):
T:= Vector(N):
for n from 1 to N do
T[M[n, n]]:= T[M[n, n]]+1;
for j from 1 to n-1 do
T[M[n, j]]:= T[M[n, j]]+2;
od:
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);
od:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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