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A166636
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Totally multiplicative sequence with a(p) = 6*(p-1) for prime p.
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1
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1, 6, 12, 36, 24, 72, 36, 216, 144, 144, 60, 432, 72, 216, 288, 1296, 96, 864, 108, 864, 432, 360, 132, 2592, 576, 432, 1728, 1296, 168, 1728, 180, 7776, 720, 576, 864, 5184, 216, 648, 864, 5184, 240, 2592, 252, 2160, 3456, 792, 276, 15552, 1296, 3456
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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) = (6*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-1)^e(k).
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MATHEMATICA
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DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=
DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*6^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (6*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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