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

1, 2, 6, 6, 30, 5, 35, 35, 35, 7, 77, 77, 1001, 143, 143, 143, 2431, 2431, 46189, 46189, 46189, 4199, 96577, 96577, 96577, 7429, 7429, 7429, 215441, 215441, 6678671, 6678671, 6678671, 392863, 392863, 392863, 14535931, 765049, 765049, 765049

Offset: 1

Author

Leroy Quet, May 06 2007

Keywords

• frac
• nonn

Comments

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

Links

• Ivan Neretin and Michael De Vlieger, Table of n, a(n) for n = 1..4642 (first 1000 terms from Ivan Neretin)

Crossrefs

Cf. A130086, A130088, A130089.

Programs

Maple

with(numtheory): a:=n->denom(product(k^mobius(k),k=1..n)): seq(a(n),n=1..50); # Emeric Deutsch, May 11 2007

Mathematica

Table[Denominator[HarmonicNumber[n]^2*(n!)],{n, 200}]
(* Second program: *)
With[{s = Array[#^MoebiusMu@ # &, 39]}, Denominator@ Table[Times @@ Take[s, n], {n, Length@ s}]] (* Michael De Vlieger, Sep 20 2017 *)

PARI

a(n)=denominator(prod(k=1,n,k^moebius(k))) \\ Charles R Greathouse IV, Mar 10 2012

Extensions

More terms from Emeric Deutsch, May 11 2007