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A167356
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Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p.
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1
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1, 0, 0, 0, 6, 0, 20, 0, 0, 0, 72, 0, 110, 0, 0, 0, 210, 0, 272, 0, 0, 0, 420, 0, 36, 0, 0, 0, 702, 0, 812, 0, 0, 0, 120, 0, 1190, 0, 0, 0, 1482, 0, 1640, 0, 0, 0, 1980, 0, 400, 0, 0, 0, 2550, 0, 432, 0, 0, 0, 3192, 0, 3422, 0, 0, 0, 660, 0, 4160, 0, 0, 0
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OFFSET
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1,5
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LINKS
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FORMULA
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Multiplicative with a(p^e) = ((p-2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)-3))^e(k).
a(2k) = 0 for k >= 1, a(3k) = 0 for k >= 1.
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 4/p^2 - 1/p^3 - 6/p^4) = 0.073139277512... . - 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]] - 2)^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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nonn,mult
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AUTHOR
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STATUS
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approved
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