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A190585 E.g.f. prod(n>=1, (1-x^n)^(-u(n)/n) where u(n) is the unitary Moebius function (A076479). 4
1, 1, 1, 1, -5, -29, -89, -209, -9239, -120455, -801359, -3674879, 15450931, 505760971, 4925214295, 30957618511, -3280733667119, -49063880680079, -327527326905119, -1087577476736255, 97366167074820331, 1723137650565888691, 13360549076712501511 (list; graph; refs; listen; history; text; internal format)
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

Cf. A076479.

Sequence in context: A111937 A215850 A308396 * A197276 A211062 A264750

Adjacent sequences:  A190582 A190583 A190584 * A190586 A190587 A190588

KEYWORD

sign

AUTHOR

Joerg Arndt, May 13 2011

STATUS

approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)