cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A103223 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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%I A103223 #13 Feb 21 2020 07:06:56
%S A103223 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,
%T A103223 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,
%U A103223 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
%N A103223 Imaginary part of the totient function phi(n) for Gaussian integers. See A103222 for the real part and A103224 for the norm.
%C A103223 Note that a(n)=0 when n is in A004614, the product of real Gaussian primes. It appears that all terms are nonnegative.
%H A103223 Amiram Eldar, <a href="/A103223/b103223.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%t A103223 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}]]
%Y A103223 Cf. A103222, A103224.
%K A103223 nonn
%O A103223 1,4
%A A103223 _T. D. Noe_, Jan 26 2005