cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A080306 #8 Nov 13 2021 15:14:30
%S A080306 1,3,11,17,91,271,1927,2137,2347,4447,49127,51437,670991,1091411,
%T A080306 1541861,1571891,26752177,27262687,518501563,528201253,731894743,
%U A080306 945287923,21751321919,21974414789,22197507659,27997922279,28221015149
%N A080306 Numerator of Sum(k^mu(k): 1<=k<=n), where mu is the Moebius function (A008683).
%e A080306 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 A080306 Accumulate[Table[n^MoebiusMu[n],{n,30}]]//Numerator (* _Harvey P. Dale_, Nov 13 2021 *)
%o A080306 (PARI) a(n) = numerator(sum(k = 1, n, k^moebius(k))); \\ _Michel Marcus_, Aug 29 2013
%Y A080306 Denominators are in A080326. Cf. A080304, A080305.
%K A080306 nonn,frac
%O A080306 1,2
%A A080306 _Reinhard Zumkeller_, Feb 13 2003