OFFSET
0,5
COMMENTS
The corresponding sequence for the (usual) Moebius function is the constant sequence a(n)=1 (A000012).
Log(e.g.f.) = x - (1/4)*x^4 - (1/4)*x^8 - (1/9)*x^9 - (3/16)*x^16 - (1/25)*x^25 - (2/27)*x^27 - (1/8)*x^32 + (1/36)*x^36 - (1/49)*x^49 - (5/64)*x^64 +- ...; the corresponding function for the usual Moebius function is log(exp(x)) = x.
Log(g.f.) = x + (1/2)*x^2 + (1/3)*x^3 - (23/4)*x^4 - (119/5)*x^5 - (359/6)*x^6 - (839/7)*x^7 +- ...; the corresponding function for the usual Moebius function if Sum_{n>=1} h(n)*x^n where h(n) = Sum_{k=1..n} 1/k is a harmonic number.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..65
PROG
(PARI)
N=66; /* that many terms */
/* First compute the unitary Moebius function */
mu=vector(N); mu[1]=1;
{ for (n=2, N,
s = 0;
fordiv (n, d,
if (gcd(d, n/d)!=1, next() ); /* unitary divisors only */
s += mu[d];
);
mu[n] = -s;
); };
egf=prod(n=1, N, (1-x^n)^(-mu[n]/n)); /* = 1 +x +1/2*x^2 +1/6*x^3 -5/24*x^4 +-... */
Vec(serlaplace(egf)) /* show terms */
CROSSREFS
KEYWORD
sign
AUTHOR
Joerg Arndt, May 13 2011
STATUS
approved