A174940 a(n) = Sum_{d|n} A007955(d) * A008683(n/d) = Sum_{d|n} A007955(d) * mu(n/d), where A007955(m) = number of divisors of m.

1, 1, 2, 6, 4, 32, 6, 56, 24, 94, 10, 1686, 12, 188, 218, 960, 16, 5772, 18, 7894, 432, 472, 22, 329992, 120, 662, 702, 21750, 28, 809648, 30, 31744, 1076, 1138, 1214, 10070172, 36, 1424, 1506, 2551944, 40, 3111034, 42, 84694, 90876, 2092, 46, 254471232, 336, 124780

Offset: 1

Author

Jaroslav Krizek, Apr 02 2010

Keywords

• nonn

Examples

			For n = 4, A007955(n) = b(n): a(4) = b(1)*mu(4/1) + b(2)*mu(4/2) + b(4)*mu(4/4) = 1*0 + 2*(-1) + 8*1 = 6.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008683 (mu), A007955 (product of divisors).

Programs

Magma

[&+[&*Divisors(d)*MoebiusMu(n div d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Jan 05 2020

Mathematica

a[n_] := Sum[ MoebiusMu[n/d] * Times @@ Divisors[d], {d, Divisors[n]} ]; Table[ a[n], {n, 1, 30} ] (* Jean-François Alcover, Jan 09 2013 *)

PARI

a(n)={sumdiv(n, d, vecprod(divisors(d))*moebius(n/d))} \\ Andrew Howroyd, Jan 05 2020

Formula

Moebius transform of A007955. - Andrew Howroyd, Jan 05 2020

Extensions

Terms a(31) and beyond from Andrew Howroyd, Jan 05 2020