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 A257477 Multiplicative with a(2) = 0, a(4) = -1, a(2^e) = 0 if e>2, a(3) = -1, a(3^e) = 0^e if e>1, a(p^e) = 1 if p == 1, 3 (mod 8), a(p^e) = (-1)^e if p == 5, 7 (mod 8). 2
 1, 0, -1, -1, -1, 0, -1, 0, 0, 0, 1, 1, -1, 0, 1, 0, 1, 0, 1, 1, 1, 0, -1, 0, 1, 0, 0, 1, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, -1, 0, 0, -1, 0, 1, 0, -1, 1, -1, 0, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 1, 0, 1, -1, 1, 0, -1, 0, 1, 0, -1, -1, -1, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..2500 FORMULA G.f.: f(x) - 2*f(x^3) - f(x^4) + f(x^9) + 2*f(x^12) - f(x^36) where f(x) = (x + x^3) / (1 + x^4) is the g.f. for A188510. abs(a(2*n + 1)) = A168182(n+5). a(4*n + 2) = a(8*n) = a(9*n) = 0. a(n) = -a(-n) = a(n + 288) for all n in Z. Moebius transform of A257403. EXAMPLE G.f. = x - x^3 - x^4 - x^5 - x^7 + x^11 + x^12 - x^13 + x^15 + x^17 + ... MATHEMATICA a[ n_] := Sign[n] If[ Abs[n] < 2, 1, Times @@ (Which[ # < 5, -Boole[# + #2 == 4], Mod[#, 8] < 4, 1, True, (-1)^#2] & @@@ FactorInteger[Abs@n])]; f[x_] := (x + x^3)/(1 + x^4); CoefficientList[Series[f[x] - 2*f[x^3] - f[x^4] + f[x^9] + 2*f[x^12] - f[x^36], {x, 0, 50}], x] (* G. C. Greubel, Aug 03 2018 *) PROG (PARI) {a(n) = my(A, p, e); if( n==0, 0, A = factor(abs(n)); sign(n) * prod( k=1, matsize(A)[1], [p, e] = A[k, ]; if( p<5, -(p+e==4), if( p%8 < 4, 1, (-1)^e))))}; CROSSREFS Cf. A168182, A188510, A257403. Sequence in context: A267800 A322980 A267053 * A259024 A323045 A104106 Adjacent sequences:  A257474 A257475 A257476 * A257478 A257479 A257480 KEYWORD sign,mult AUTHOR Michael Somos, Apr 25 2015 EXTENSIONS Definition corrected by Georg Fischer, Jul 23 2022 STATUS approved

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Last modified August 8 16:31 EDT 2022. Contains 356016 sequences. (Running on oeis4.)