A174943 a(n) = Sum_{k<=n} A007955(k) * A008683(k) = Sum_{k<=n} A007955(k) * mu(k), where A007955(m) = product of divisors of m.

1, -1, -4, -4, -9, 27, 20, 20, 20, 120, 109, 109, 96, 292, 517, 517, 500, 500, 481, 481, 922, 1406, 1383, 1383, 1383, 2059, 2059, 2059, 2030, -807970, -808001, -808001, -806912, -805756, -804531, -804531, -804568, -803124, -801603, -801603, -801644, -3913340, -3913383

Offset

1,3

Links

Table of n, a(n) for n=1..43.

Example

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.

Mathematica

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

Crossrefs

Cf. A007955, A008683.

Sequence in context: A089539 A324010 A117416 * A173317 A059811 A202409

Adjacent sequences: A174940 A174941 A174942 * A174944 A174945 A174946

Keyword

sign,changed

Author

Jaroslav Krizek, Apr 02 2010

Extensions

More terms from Amiram Eldar, Aug 06 2024

Status

approved