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Denominator of Sum(k^mu(k): 1<=k<=n), where mu is the Moebius function (A008683).
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%I #10 Jul 28 2021 18:53:38

%S 1,2,6,6,30,30,210,210,210,210,2310,2310,30030,30030,30030,30030,

%T 510510,510510,9699690,9699690,9699690,9699690,223092870,223092870,

%U 223092870,223092870,223092870,223092870,6469693230,3234846615

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

%C a(n) is a divisor of A034386(n), the product of the primes <= n. Does a(n) = A034386(n) for infinitely many n?

%H Harvey P. Dale, <a href="/A080326/b080326.txt">Table of n, a(n) for n = 1..1000</a>

%t Accumulate[Table[n^MoebiusMu[n],{n,30}]]//Denominator (* _Harvey P. Dale_, Jul 28 2021 *)

%o (PARI) a(n) = denominator(sum(k = 1, n, k^moebius(k))); \\ _Michel Marcus_, Aug 29 2013

%Y Numerators are in A080306. Cf. A080304, A080305, A034386.

%K nonn,frac

%O 1,2

%A _Dean Hickerson_, Feb 15 2003