A085411 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for 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

MATHEMATICA

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

CROSSREFS

Cf. A001792, A000740.

Cf. A007318, A054525.

Sequence in context: A178441 A014742 A367687 * A180665 A275209 A007049

Adjacent sequences: A085408 A085409 A085410 * A085412 A085413 A085414

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 13 2003

EXTENSIONS

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

STATUS

approved