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A167346
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Totally multiplicative sequence with a(p) = (p-1)*(p+2) = p^2+p-2 for prime p.
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1
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1, 4, 10, 16, 28, 40, 54, 64, 100, 112, 130, 160, 180, 216, 280, 256, 304, 400, 378, 448, 540, 520, 550, 640, 784, 720, 1000, 864, 868, 1120, 990, 1024, 1300, 1216, 1512, 1600, 1404, 1512, 1800, 1792, 1720, 2160, 1890, 2080, 2800, 2200, 2254, 2560, 2916, 3136
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OFFSET
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1,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..1000
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FORMULA
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Multiplicative with a(p^e) = ((p-1)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+2))^e(k). a(n) = A003958(n) * A166590(n).
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + p - 3)) = 1.611922780552146990915794949248803526278171368254928942581015265238806543... - Vaclav Kotesovec, Sep 20 2020
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MATHEMATICA
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a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)
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CROSSREFS
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Sequence in context: A112984 A191115 A073121 * A307274 A027430 A298031
Adjacent sequences: A167343 A167344 A167345 * A167347 A167348 A167349
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KEYWORD
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nonn,mult
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AUTHOR
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Jaroslav Krizek, Nov 01 2009
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STATUS
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approved
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