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A103224 Norm of the totient function phi(n) for Gaussian integers. See A103222 and A103223 for the real and imaginary parts. 4
1, 2, 4, 8, 8, 8, 36, 32, 36, 16, 100, 32, 80, 72, 32, 128, 160, 72, 324, 64, 144, 200, 484, 128, 200, 160, 324, 288, 520, 64, 900, 512, 400, 320, 288, 288, 936, 648, 320, 256, 1088, 288, 1764, 800, 288, 968, 2116, 512, 1764, 400, 640, 640, 2000, 648, 800, 1152 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A103222 for definitions.

Multiplicative because the totient function on Gaussian integers is multiplicative and the norm is completely multiplicative. - Andrew Howroyd, Aug 03 2018

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

a(n) = A103222(n)^2 + A103223(n)^2. - Andrew Howroyd, Aug 03 2018

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]]; Abs[Table[phi[n], {n, 100}]]^2

PROG

(PARI) \\ See A103222

CEulerPhi(z)={my(f=factor(z, I)); prod(i=1, #f~, my([p, e]=f[i, ]); if(norm(p)==1, p^e, (p-1)*p^(e-1)))}

a(n)=norm(CEulerPhi(n)); \\ Andrew Howroyd, Aug 03 2018

CROSSREFS

Cf. A103222, A103223, A103230.

Sequence in context: A172305 A187221 A129280 * A198346 A078750 A054785

Adjacent sequences:  A103221 A103222 A103223 * A103225 A103226 A103227

KEYWORD

nonn,mult

AUTHOR

T. D. Noe, Jan 26 2005

STATUS

approved

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Last modified January 29 08:12 EST 2020. Contains 331337 sequences. (Running on oeis4.)