%I #8 Nov 13 2021 15:14:30
%S 1,3,11,17,91,271,1927,2137,2347,4447,49127,51437,670991,1091411,
%T 1541861,1571891,26752177,27262687,518501563,528201253,731894743,
%U 945287923,21751321919,21974414789,22197507659,27997922279,28221015149
%N Numerator of Sum(k^mu(k): 1<=k<=n), where mu is the Moebius function (A008683).
%e 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.
%t Accumulate[Table[n^MoebiusMu[n],{n,30}]]//Numerator (* _Harvey P. Dale_, Nov 13 2021 *)
%o (PARI) a(n) = numerator(sum(k = 1, n, k^moebius(k))); \\ _Michel Marcus_, Aug 29 2013
%Y Denominators are in A080326. Cf. A080304, A080305.
%K nonn,frac
%O 1,2
%A _Reinhard Zumkeller_, Feb 13 2003