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A167314
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Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.
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1
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1, -4, 0, 16, 8, 0, 16, -64, 0, -32, 32, 0, 40, -64, 0, 256, 56, 0, 64, 128, 0, -128, 80, 0, 64, -160, 0, 256, 104, 0, 112, -1024, 0, -224, 128, 0, 136, -256, 0, -512, 152, 0, 160, 512, 0, -320, 176, 0, 256, -256, 0, 640, 200, 0, 256, -1024, 0, -416, 224, 0, 232
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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) = (4*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(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]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
f[p_, e_] := (4*(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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