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A035154
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a(n) = sum_{d|n} kronecker( -36, d).
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9
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1, 1, 1, 1, 2, 1, 0, 1, 1, 2, 0, 1, 2, 0, 2, 1, 2, 1, 0, 2, 0, 0, 0, 1, 3, 2, 1, 0, 2, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 1, 3, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 1, 4, 0, 0, 2, 0, 0, 0, 1, 2, 2, 3, 0, 0, 2, 0, 2, 1, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 1, 2, 1, 0, 3, 2, 2, 0, 2, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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FORMULA
| Moebius transform is period 12 sequence [ 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, ...]. - Michael Somos Jul 30 2006
Multiplicative with a(2^e) = a(3^e) = 1, a(p^e) = e+1 if p == 1(mod 4), a(p^e) = (1 + (-1)^e) / 2 if p == 3(mod 4). - Michael Somos Jul 30 2006
Dirichlet g.f.: zeta(s) * L(chi,s) where chi(n) = kronecker( -36, n). Sum_{n>0} a(n) / n^s = Product_{p prime} 1 / ((1 - p^-s) * (1 - kronecker( -36, p) * p^-s)). - Michael Somos Jun 24 2011 */
a(2*n) = a(3*n) = a(n). a(2*n + 1) = A125079(n). a(3*n + 1) = A122865(n). a(3*n + 2) = A122856(n). a(4*n + 1) = A008441(n).
G.f.: Sum_{n>=0} (-1)^n*( x^(6*n+1)/(1-x^(6*n+1)) + x^(6*n+5)/(1-x^(6*n+5)) ). [From Paul D. Hanna, Dec 14 2011]
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EXAMPLE
| G.f.: x + x^2 + x^3 + x^4 + 2*x^5 + x^6 + x^8 + x^9 + 2*x^10 + x^12 + 2*x^13 + ...
G.f.: x/(1-x) + x^5/(1-x^5) - x^7/(1-x^7) - x^11/(1-x^11) + x^13/(1-x^13) + x^17/(1-x^17) --++...
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MATHEMATICA
| a[ n_] := If[ n < 1, 0, Sum[ KroneckerSymbol[ -36, d], { d, Divisors[ n]}]] (* Michael Somos Jun 24 2011 *)
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PROG
| (PARI) {a(n) = if( n<1, 0, sumdiv(n, d, kronecker( -36, d)))} /* Michael Somos Jul 30 2006 */
(PARI) {a(n) = if( n<1, 0, direuler(p=2, n, 1 / ((1 - X) * (1 - kronecker( -36, p) * X))) [n])} /* Michael Somos Jul 30 2006 */
(PARI) {a(n)=polcoeff(sum(m=0, n\6+1, (-1)^m*(x^(6*m+1)/(1-x^(6*m+1)+x*O(x^n)) + x^(6*m+5)/(1-x^(6*m+5)+x*O(x^n)))), n)} /* Paul D. Hanna */
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CROSSREFS
| Cf. A008441, A122856, A122865, A125079.
Sequence in context: * A113446 A121450 A132004 A143110 A109294 A132966
Adjacent sequences: A035151 A035152 A035153 * A035155 A035156 A035157
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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