A140664 - OEIS

%I #9 Feb 15 2019 23:42:00

%S 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,

%T 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,

%U 0,1,0,1,1,-59,0,-61,1,0

%N a(n) = A014963(n)*mobius(n).

%C A008683 = A140579^(-1) * A140664 - _Gary W. Adamson_, May 20 2008

%H G. C. Greubel, <a href="/A140664/b140664.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%p A140664 := proc(n)

%p         A014963(n)*numtheory[mobius](n) ;

%p end proc:

%p seq(A140664(n),n=1..80) ; # _R. J. Mathar_, Apr 05 2012

%t Table[Exp[MangoldtLambda[n]]*MoebiusMu[n], {n, 1, 75}] (* _G. C. Greubel_, Feb 15 2019 *)

%o (PARI) {a(n) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*moebius(n))};

%o vector(75, n, a(n)) \\ _G. C. Greubel_, Feb 15 2019

%o (Sage)

%o def A140664(n): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*moebius(n)

%o [A140664(n) for n in (1..75)] # _G. C. Greubel_, Feb 15 2019

%Y Cf. A140579, A014963, A008683.

%K sign

%O 1,2

%A _Gary W. Adamson_ and _Mats Granvik_, May 20 2008