A085411 Total number of parts in all compositions of n into relatively prime parts.

1, 2, 7, 17, 47, 102, 255, 556, 1272, 2766, 6143, 13183, 28671, 61182, 131017, 277952, 589823, 1243800, 2621439, 5502191, 11534073, 24111102, 50331647, 104843732, 218103760, 452956158, 939522816, 1946095599, 4026531839, 8321365194, 17179869183, 35433201664

Offset: 1

Author

Vladeta Jovovic, Aug 13 2003

Keywords

• easy
• nonn

Crossrefs

Cf. A001792, A000740.

Cf. A007318, A054525, A101391.

Programs

Mathematica

f[n_] := Block[{d = Divisors[n]}, (Plus @@ (MoebiusMu[n/d]*(d + 1)*2^(d - 2)))]; Table[ f[n], {n, 1, 30}]

Formula

Sum_{d|n} mu(n/d)*(d+1)*2^(d-2).

G.f.: Sum_{k>=0} mu(k)*x^k*(1-x^k)/(1-2*x^k)^2.

Equals A054525 * A007318 * [1,2,3,...]. - Gary W. Adamson, Jun 11 2007

a(n) = Sum_{k=1..n} k * A101391(n,k). - Alois P. Heinz, May 05 2025

Extensions

More terms from Robert G. Wilson v, Aug 15 2003