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A167313
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Totally multiplicative sequence with a(p) = 3*(p-3) for prime p.
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1
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1, -3, 0, 9, 6, 0, 12, -27, 0, -18, 24, 0, 30, -36, 0, 81, 42, 0, 48, 54, 0, -72, 60, 0, 36, -90, 0, 108, 78, 0, 84, -243, 0, -126, 72, 0, 102, -144, 0, -162, 114, 0, 120, 216, 0, -180, 132, 0, 144, -108, 0, 270, 150, 0, 144, -324, 0, -234, 168, 0, 174, -252, 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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Multiplicative with a(p^e) = (3*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-3))^e(k).
a(3k) = 0 for k >= 1.
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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]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
f[p_, e_] := (3*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)
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CROSSREFS
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KEYWORD
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sign,easy,mult
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AUTHOR
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STATUS
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approved
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