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Search: id:A103223
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| A103223 |
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Imaginary part of the totient function phi(n) for Gaussian integers. See A103222 for the real part and A103224 for the norm. |
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+0
3
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| 0, 1, 0, 2, 2, 2, 0, 4, 0, 4, 0, 4, 4, 6, 4, 8, 4, 6, 0, 8, 0, 10, 0, 8, 10, 12, 0, 12, 6, 8, 0, 16, 0, 16, 12, 12, 6, 18, 8, 16, 8, 12, 0, 20, 12, 22, 0, 16, 0, 20, 8, 24, 8, 18, 20, 24, 0, 28, 0, 16, 10, 30, 0, 32, 24, 20, 0, 32, 0, 24, 0, 24, 10, 36, 20, 36, 0, 24, 0, 32, 0, 40, 0, 24, 32, 42
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Note that a(n)=0 when n is in A004614, the product of real Gaussian primes. It appears that all terms are nonnegative.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
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phi[z_] := Module[{f, k, prod}, If[Abs[z]==1, z, f=FactorInteger[z, GaussianIntegers->True]; If[Abs[f[[1, 1]]]==1, k=2; prod=f[[1, 1]], k=1; prod=1]; Do[prod=prod*(f[[i, 1]]-1)f[[i, 1]]^(f[[i, 2]]-1), {i, k, Length[f]}]; prod]]; Im[Table[phi[n], {n, 100}]]
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CROSSREFS
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Sequence in context: A071442 A124759 A071295 this_sequence A091399 A000091 A155123
Adjacent sequences: A103220 A103221 A103222 this_sequence A103224 A103225 A103226
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 26 2005
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