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A167362
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Totally multiplicative sequence with a(p) = (p-3)*(p+3) = p^2-9 for prime p.
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1
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1, -5, 0, 25, 16, 0, 40, -125, 0, -80, 112, 0, 160, -200, 0, 625, 280, 0, 352, 400, 0, -560, 520, 0, 256, -800, 0, 1000, 832, 0, 952, -3125, 0, -1400, 640, 0, 1360, -1760, 0, -2000, 1672, 0, 1840, 2800, 0, -2600, 2200, 0, 1600, -1280, 0, 4000, 2800, 0, 1792
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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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Multiplicative with a(p^e) = ((p-3)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-3)*(p(k)+3))^e(k).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 - 1/p^2 + 9/p^3 + 9/p^4) = 0.05980933853... . - Amiram Eldar, Dec 15 2022
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MATHEMATICA
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a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)
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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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