A080306 Numerator of Sum(k^mu(k): 1<=k<=n), where mu is the Moebius function (A008683).

1, 3, 11, 17, 91, 271, 1927, 2137, 2347, 4447, 49127, 51437, 670991, 1091411, 1541861, 1571891, 26752177, 27262687, 518501563, 528201253, 731894743, 945287923, 21751321919, 21974414789, 22197507659, 27997922279, 28221015149

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Example

a(6) = 1^mu(1)+2^mu(2)+3^mu(3)+4^mu(4)+5^mu(5)+6^mu(6) = 1^1+2^(-1)+3^(-1)+4^0+5^(-1)+6^1 = 1 + 1/2 + 1/3 + 1 + 1/5 + 6 = (30+15+10+30+6+180)/30 = 271/30, therefore a(6)=271, A080326(6)=30.

Mathematica

Accumulate[Table[n^MoebiusMu[n], {n, 30}]]//Numerator (* Harvey P. Dale, Nov 13 2021 *)

Prog

(PARI) a(n) = numerator(sum(k = 1, n, k^moebius(k))); \\ Michel Marcus, Aug 29 2013

Crossrefs

Denominators are in A080326. Cf. A080304, A080305.

Sequence in context: A145701 A072982 A124787 * A128346 A128031 A194128

Adjacent sequences: A080303 A080304 A080305 * A080307 A080308 A080309

Keyword

nonn,frac

Author

Reinhard Zumkeller, Feb 13 2003

Status

approved