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A103223 Imaginary part of the totient function phi(n) for Gaussian integers. See A103222 for the real part and A103224 for the norm. 5
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Note that a(n)=0 when n is in A004614, the product of real Gaussian primes. It appears that all terms are nonnegative.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

MATHEMATICA

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}]]

CROSSREFS

Cf. A103222, A103224.

Sequence in context: A296062 A214178 A117652 * A091399 A350951 A263527

Adjacent sequences: A103220 A103221 A103222 * A103224 A103225 A103226

KEYWORD

nonn

AUTHOR

T. D. Noe, Jan 26 2005

STATUS

approved

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Last modified December 1 11:19 EST 2022. Contains 358468 sequences. (Running on oeis4.)