A117208 G.f. A(x) satisfies (1-x) = product_{n>=1} A(x^n).

1, -1, 1, 0, 0, 1, -1, 2, -1, 1, 0, 1, 0, 1, 0, 0, 2, -1, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 0, 3, 0, 0, 2, 0, 3, 0, 3, -1, 2, 0, 4, 1, 1, 3, -3, 5, 1, 3, 0, 2, -1, 2, 4, 2, 4, -5, 6, -1, 2, 7, -2, 1, -1, 4, 3, 5, 2, -2, 1, 1, 8, 2, 4, -1, -3, 4, 9, 4, -2, 4, -7, 6, 7, 10, -1, -3, -1, 1, 11, 4, 8, -15, 2, 5, 7, 13, 1, -9, -7, 9

Offset

0,8

Comments

Self-convolution inverse is A117209.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x) = exp( -Sum_{n>=1} A023900(n)*x^n/n ), where A023900 is the Dirichlet inverse of Euler totient function.

Euler transform of the negative of the Möbius function. - Stuart Clary, Apr 15 2006

G.f.: A(x) = product_{k>=1}(1 - x^k)^mu(k) where mu(k) is the Möbius function, A008683. - Stuart Clary, Apr 15 2006

Mathematica

nmax = 106; CoefficientList[ Series[ Product[ (1 - x^k)^(MoebiusMu[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ] (* Stuart Clary, Apr 15 2006 *)

Prog

(PARI) {a(n)=polcoeff(exp(-sum(k=1, n+1, sumdiv(k, d, d*moebius(d))*x^k/k)+x*O(x^n)), n)}

Crossrefs

Cf. A023900 (l.g.f.), A117209 (inverse); variants: A117210, A117211, A117212.

Sequence in context: A342531 A287156 A092510 * A276004 A133300 A337101

Adjacent sequences: A117205 A117206 A117207 * A117209 A117210 A117211

Keyword

sign

Author

Paul D. Hanna, Mar 03 2006

Status

approved