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%I #19 Mar 30 2024 03:00:33
%S 1,1,3,4,5,5,7,12,9,9,11,20,13,13,15,32,17,21,19,36,21,21,23,60,25,25,
%T 27,52,29,45,31,80,33,33,35,84,37,37,39,108,41,65,43,84,45,45,47,160,
%U 49,65,51,100,53,81,55,156,57,57,59,180,61,61,63,192,65,105
%N a(n) = Sum_{k=1..n} (-1)^(n-k) gcd(k,n).
%H Felix Fröhlich, <a href="/A344371/b344371.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = abs(A199084(n)).
%F a(2n+1) = 2n+1.
%F a(2n) = A344372(n) = 2*n - A106475(n-1).
%F Sum_{k=1..n} a(k) ~ (n^2/Pi^2) * (log(n) + 2*gamma - 1/2 - 4*log(2)/3 + Pi^2/4 - zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Mar 30 2024
%o (PARI) a(n) = sum(k=1, n, (-1)^(n-k)*gcd(k,n)); \\ _Michel Marcus_, May 16 2021
%Y Cf. A001620, A090423, A106475, A199084, A306016, A344372, A344373.
%K nonn,easy
%O 1,3
%A _Max Alekseyev_, May 16 2021
%E More terms from _Felix Fröhlich_, May 19 2021
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