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A167357
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Totally multiplicative sequence with a(p) = (p-2)*(p+3) = p^2+p-6 for prime p.
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1
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1, 0, 6, 0, 24, 0, 50, 0, 36, 0, 126, 0, 176, 0, 144, 0, 300, 0, 374, 0, 300, 0, 546, 0, 576, 0, 216, 0, 864, 0, 986, 0, 756, 0, 1200, 0, 1400, 0, 1056, 0, 1716, 0, 1886, 0, 864, 0, 2250, 0, 2500, 0, 1800, 0, 2856, 0, 3024, 0, 2244, 0, 3534, 0, 3776, 0, 1800
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OFFSET
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1,3
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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.
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 - 2/p^2 + 5/p^3 + 6/p^4) = 0.1449357432... . - 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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