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

1,2

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)

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 *)

Prog

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

Crossrefs

Cf. A130086, A130088, A130089.

Sequence in context: A105725 A005226 A087310 * A085087 A072983 A055204

Adjacent sequences: A130084 A130085 A130086 * A130088 A130089 A130090

Keyword

frac,nonn

Author

Leroy Quet, May 06 2007

Extensions

More terms from Emeric Deutsch, May 11 2007

Status

approved