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

Author

Reinhard Zumkeller, Feb 13 2003

Keywords

• nonn
• frac

Examples

			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.
		

Crossrefs

Denominators are in A080326. Cf. A080304, A080305.

Programs

Mathematica

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

PARI

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