A174943 - OEIS

%I #7 Aug 06 2024 02:07:10

%S 1,-1,-4,-4,-9,27,20,20,20,120,109,109,96,292,517,517,500,500,481,481,

%T 922,1406,1383,1383,1383,2059,2059,2059,2030,-807970,-808001,-808001,

%U -806912,-805756,-804531,-804531,-804568,-803124,-801603,-801603,-801644,-3913340,-3913383

%N a(n) = Sum_{k<=n} A007955(k) * A008683(k) = Sum_{k<=n} A007955(k) * mu(k), where A007955(m) = product of divisors of m.

%e For n = 4, A007955(n) = b(n): a(4) = b(1)*mu(1) + b(2)*mu(2) + b(3)* mu(3) + b(4)*mu(4) = 1*1 + 2*(-1) + 3*(-1) + 8*0 = -4.

%t a[n_] := Sum[k^(DivisorSigma[0, k]/2) * MoebiusMu[k], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Aug 06 2024 *)

%Y Cf. A007955, A008683.

%K sign

%O 1,3

%A _Jaroslav Krizek_, Apr 02 2010

%E More terms from _Amiram Eldar_, Aug 06 2024