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A018806
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Sum of gcd(x, y) for 1 <= x, y <= n.
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12
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1, 5, 12, 24, 37, 61, 80, 112, 145, 189, 220, 288, 325, 389, 464, 544, 593, 701, 756, 880, 989, 1093, 1160, 1336, 1441, 1565, 1700, 1880, 1965, 2205, 2296, 2488, 2665, 2829, 3028, 3328, 3437, 3621, 3832, 4152, 4273, 4621, 4748, 5040, 5373, 5597, 5736, 6168
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OFFSET
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1,2
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COMMENTS
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a(n) is also the entrywise 1-norm of the n X n GCD matrix.
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LINKS
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FORMULA
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G.f.: sum(k >= 1, phi(k)*x^k*(1+x^k)/((1-x^k)^2*(1-x)). - Robert Israel, Jan 14 2015
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MAPLE
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N:= 1000 # to get a(1) to a(N)
g:= add(numtheory:-phi(k)*x^k*(1+x^k)/((1-x^k)^2*(1-x)), k=1..N):
S:= series(g, x, N+1):
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MATHEMATICA
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Table[nn = n; Total[Level[Table[Table[GCD[i, j], {i, 1, nn}], {j, 1, nn}], {2}]], {n, 1, 48}] (* Geoffrey Critzer, Jan 14 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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