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%I #19 May 29 2021 09:00:33
%S 1,7,28,72,177,303,604,948,1497,2127,3348,4272,6313,8119,10324,13060,
%T 17701,20995,27512,32132,38453,45779,57440,64664,77689,89935,104704,
%U 117948,141525,154755,183616,205472,231113,258959,290564,314720,364041
%N Sum of lcm(x, y) for 1 <= x, y <= n.
%C a(n) is also the entrywise 1-norm of the n X n LCM matrix.
%H Harry J. Smith, <a href="/A064951/b064951.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = a(n-1) + 2*A051193(n) - n = a(n-1) + n*A057660(n) = Sum_{1 <= i <= j <= n} (j^2/gcd(i, j)). - _Henry Bottomley_, Oct 29 2001
%F a(n) ~ 3 * zeta(3) * n^4 / (2*Pi^2). - _Vaclav Kotesovec_, May 29 2021
%t Table[nn = n;Total[Level[Table[Table[LCM[i, j], {i, 1, nn}], {j, 1, nn}], {2}]], {n, 1, 37}] (* _Geoffrey Critzer_, Jan 14 2015 *)
%o (PARI) { a=0; for (n=1, 1000, a+=n*sum(k=1, n, n/gcd(n, k)); write("b064951.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 01 2009
%Y Cf. A018806.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Oct 28 2001
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