%I #9 Feb 11 2020 03:54:26
%S 4,5,35,51,154,804,3596,6200,7595,916538,1638039,2794805,6804035,
%T 24724472,40128444,52424787,69918849,82954611,124077316,160245605,
%U 204215514,361275551,371254235,661831521,1314759754,1695554762,2246110022,2378746131,2889320799,4181707719
%N Numbers k such that k and k + 1 have the same value of the norm of the totient function for Gaussian integers (A103224).
%C The corresponding common values A103224(k) = A103224(k+1) are 8, 8, 288, 640, 7200, 139392, 3744000, 5760000, ...
%H Amiram Eldar, <a href="/A332316/b332316.txt">Table of n, a(n) for n = 1..37</a>
%e 4 is a term since norm(phi(4)) = norm(phi(5)) = 8.
%t 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]]; Select[Range[10^3], Abs[phi[#]]^2 == Abs[phi[# + 1]]^2 &] (* after _T. D. Noe_ at A103222 *)
%Y Cf. A001274, A103222, A103223, A103224, A287055, A293184, A326403.
%K nonn
%O 1,1
%A _Amiram Eldar_, Feb 09 2020