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A130087 Denominator of product{k=1 to n} k^mu(k), where mu is the Moebius function A008683. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)