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A308077
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G.f. A(x) satisfies: A(x) = x - A(x^2) + A(x^3) - A(x^4) + A(x^5) - A(x^6) + ...
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8
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1, -1, 1, 0, 1, -3, 1, 0, 2, -3, 1, 2, 1, -3, 3, 0, 1, -8, 1, 2, 3, -3, 1, 0, 2, -3, 4, 2, 1, -13, 1, 0, 3, -3, 3, 10, 1, -3, 3, 0, 1, -13, 1, 2, 8, -3, 1, 0, 2, -8, 3, 2, 1, -20, 3, 0, 3, -3, 1, 18, 1, -3, 8, 0, 3, -13, 1, 2, 3, -13, 1, -4, 1, -3, 8, 2, 3, -13, 1
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OFFSET
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1,6
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LINKS
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FORMULA
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a(1) = 1; a(n) = Sum_{d|n, d<n} (-1)^(n/d+1)*a(d).
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n, add(a(n/d)*
(-1)^(d-1), d=numtheory[divisors](n) minus {1}))
end:
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MATHEMATICA
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terms = 79; A[_] = 0; Do[A[x_] = x + Sum[(-1)^(k + 1) A[x^k], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
a[n_] := If[n == 1, n, Sum[If[d < n, (-1)^(n/d + 1) a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 79}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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