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A359485
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a(1) = 1, a(2) = -5; a(n) = -n^2 * Sum_{d|n, d < n} a(d) / d^2.
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5
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1, -5, -9, 4, -25, 45, -49, 0, 0, 125, -121, -36, -169, 245, 225, 0, -289, 0, -361, -100, 441, 605, -529, 0, 0, 845, 0, -196, -841, -1125, -961, 0, 1089, 1445, 1225, 0, -1369, 1805, 1521, 0, -1681, -2205, -1849, -484, 0, 2645, -2209, 0, 0, 0, 2601, -676, -2809, 0, 3025, 0, 3249, 4205, -3481, 900, -3721, 4805, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) is multiplicative with a(2)= -5, a(4)= 4, a(2^e)= 0 if e>2. a(p)= -p^2, a(p^e)= 0 if e>1, p>2.
G.f. A(x) satisfies x * (1 - x) = Sum_{k>=1} k^2 * A(x^k).
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MATHEMATICA
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f[p_, e_] := If[e == 1, -p^2, 0]; f[2, e_] := Switch[e, 1, -5, 2, 4, _, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 10 2023 *)
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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