A140664 a(n) = A014963(n)*mobius(n).

1, -2, -3, 0, -5, 1, -7, 0, 0, 1, -11, 0, -13, 1, 1, 0, -17, 0, -19, 0, 1, 1, -23, 0, 0, 1, 0, 0, -29, -1, -31, 0, 1, 1, 1, 0, -37, 1, 1, 0, -41, -1, -43, 0, 0, 1, -47, 0, 0, 0, 1, 0, -53, 0, 1, 0, 1, 1, -59, 0, -61, 1, 0

Offset: 1

Author

Gary W. Adamson and Mats Granvik, May 20 2008

Keywords

• sign

Comments

A008683 = A140579^(-1) * A140664 - Gary W. Adamson, May 20 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A140579, A014963, A008683.

Programs

Maple

A140664 := proc(n)
        A014963(n)*numtheory[mobius](n) ;
end proc:
seq(A140664(n),n=1..80) ; # R. J. Mathar, Apr 05 2012

Mathematica

Table[Exp[MangoldtLambda[n]]*MoebiusMu[n], {n, 1, 75}] (* G. C. Greubel, Feb 15 2019 *)

PARI

{a(n) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*moebius(n))};
vector(75, n, a(n)) \\ G. C. Greubel, Feb 15 2019

Sage

def A140664(n): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*moebius(n)
[A140664(n) for n in (1..75)] # G. C. Greubel, Feb 15 2019

Formula

A140579 as an infinite lower triangular matrix * A008683 as a vector, where A008683 = the mu sequence and A140579 is a diagonalized matrix version of A014963. Given the A008683, the mu sequence (1, -1, -1, 0, -1, 1, -1, 0, 0, 1,...), replace (-1) with (-n). Other mu(n) remain the same.