A117209 G.f. A(x) satisfies 1/(1-x) = Product_{k>=1} A(x^k).

1, 1, 0, -1, -1, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 2, -1, -1, -2, 0, 1, 3, -1, 0, -1, 1, -1, 1, -3, 1, -1, 1, -2, 3, 0, 6, -1, -1, -6, 2, -4, 4, -3, 2, -4, 6, -5, 6, -2, 7, -5, 4, -13, 5, -3, 11, -6, 8, -14, 10, -6, 9, -14, 11, -14, 15, -13, 9, -15, 24, -13, 19, -21, 12, -20, 27, -24, 21, -26, 22, -24, 33, -33, 32, -26

Offset

0,17

Comments

Self-convolution inverse is A117208.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Paul D. Hanna)

N. J. A. Sloane, Transforms

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 Möbius function A008683. - Stuart Clary, Franklin T. Adams-Watters and Vladeta Jovovic, 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 and Franklin T. Adams-Watters, Apr 15 2006

G.f.: A(x) = Product_{k>=1} (1 + x^(2*k-1))^mu(2*k-1), where mu() is the Moebius function. - Seiichi Manyama, Jul 06 2024

Mathematica

nmax = 85; 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.), A117208 (inverse); variants: A117210, A117211, A117212.

Cf. A008683.

Sequence in context: A342149 A224326 A096496 * A035192 A229653 A089062

Adjacent sequences: A117206 A117207 A117208 * A117210 A117211 A117212

Keyword

sign

Author

Paul D. Hanna, Mar 03 2006

Status

approved