login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103224 Norm of the totient function phi(n) for Gaussian integers. See A103222 and A103223 for the real and imaginary parts. 6
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

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)