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A117208
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G.f. A(x) satisfies: (1-x) = product_{n>=1} A(x^n).
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Self-convolution inverse is A117209.
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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 Moebius (Mobius) function - Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
G.f.: A(x) = product_{k>=1}(1 - x^k)^mu(k) where mu(k) is the Moebius (Mobius) function, A008683 - Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
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MATHEMATICA
| nmax = 106; CoefficientList[ Series[ Product[ (1 - x^k)^(MoebiusMu[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ] - Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
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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)}
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CROSSREFS
| Cf. A023900 (log.g.f.), A117209 (inverse); variants: A117210, A117211, A117212.
Sequence in context: A145679 A007273 A016319 * A133300 A178779 A144451
Adjacent sequences: A117205 A117206 A117207 * A117209 A117210 A117211
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2006
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