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A118206 Euler transform of the Liouville function. 6
1, 1, 0, -1, 0, 0, 0, -1, -1, 0, 2, 0, -2, -2, 1, 2, 2, -2, -2, 0, 2, -1, -1, -2, 2, 5, 4, -5, -5, -2, 4, 2, -2, -7, 3, 8, 5, -7, -6, 1, 14, 4, -9, -14, 2, 5, 5, -10, -7, 6, 22, 3, -12, -20, 1, 15, 15, -16, -12, 4, 25, 6, -14, -31, 13, 33, 14, -39, -32, -6, 39, 15, -20, -31, 33, 41, 14, -53, -44, 3, 66, 12, -35, -51, 22, 48, 36, -60, -43, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

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

FORMULA

G.f.: A(x) = product_{k>=1}(1 - x^k)^(-lambda(k)) where lambda(k) is the Liouville function, A008836.

Logarithmic derivative yields A061020. - Paul D. Hanna, Sep 22 2011

MATHEMATICA

nmax = 100; lambda[k_Integer?Positive] := If[ k > 1, (-1)^Total[ Part[Transpose[FactorInteger[k]], 2] ], 1 ]; CoefficientList[ Series[ Product[ (1 - x^k)^(-lambda[k]), {k, 1, nmax} ], {x, 0, nmax} ], x ]

max = 100; s = Product[(1 - x^k)^(-LiouvilleLambda[k]), {k, 1, max}] + O[x]^max; CoefficientList[s, x] (* Jean-Fran├žois Alcover, Dec 23 2015 *)

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sumdiv(m, d, d*moebius(core(d)))*x^m/m)+x*O(x^n)), n)} /* Cf. A061020 - Paul D. Hanna, Sep 22 2011 */

CROSSREFS

Cf. A118205, A118207, A118208, A061020, A117209.

Sequence in context: A023604 A219660 A060964 * A029314 A071635 A156643

Adjacent sequences:  A118203 A118204 A118205 * A118207 A118208 A118209

KEYWORD

sign,easy

AUTHOR

Stuart Clary, Apr 15 2006

STATUS

approved

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Last modified December 6 19:22 EST 2019. Contains 329809 sequences. (Running on oeis4.)