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A130087 Denominator of product{k=1 to n} k^mu(k), where mu is the Moebius function A008683.

%I A130087 #29 Feb 28 2022 12:09:36
%S A130087 1,2,6,6,30,5,35,35,35,7,77,77,1001,143,143,143,2431,2431,46189,46189,
%T A130087 46189,4199,96577,96577,96577,7429,7429,7429,215441,215441,6678671,
%U A130087 6678671,6678671,392863,392863,392863,14535931,765049,765049,765049
%N A130087 Denominator of product{k=1 to n} k^mu(k), where mu is the Moebius function A008683.
%C A130087 a(n) is also the denominator of H(n)^2 * n! for all n < 897, where H(n) = 1 + 1/2 + ... + 1/n is the n-th harmonic number. - _John M. Campbell_, May 13 2011
%H A130087 Ivan Neretin and Michael De Vlieger, <a href="/A130087/b130087.txt">Table of n, a(n) for n = 1..4642</a> (first 1000 terms from Ivan Neretin)
%p A130087 with(numtheory): a:=n->denom(product(k^mobius(k),k=1..n)): seq(a(n),n=1..50); # _Emeric Deutsch_, May 11 2007
%t A130087 Table[Denominator[HarmonicNumber[n]^2*(n!)],{n, 200}]
%t A130087 (* Second program: *)
%t A130087 With[{s = Array[#^MoebiusMu@ # &, 39]}, Denominator@ Table[Times @@ Take[s, n], {n, Length@ s}]] (* _Michael De Vlieger_, Sep 20 2017 *)
%o A130087 (PARI) a(n)=denominator(prod(k=1,n,k^moebius(k))) \\ _Charles R Greathouse IV_, Mar 10 2012
%Y A130087 Cf. A130086, A130088, A130089.
%K A130087 frac,nonn
%O A130087 1,2
%A A130087 _Leroy Quet_, May 06 2007
%E A130087 More terms from _Emeric Deutsch_, May 11 2007