A332316 Numbers k such that k and k + 1 have the same value of the norm of the totient function for Gaussian integers (A103224).

4, 5, 35, 51, 154, 804, 3596, 6200, 7595, 916538, 1638039, 2794805, 6804035, 24724472, 40128444, 52424787, 69918849, 82954611, 124077316, 160245605, 204215514, 361275551, 371254235, 661831521, 1314759754, 1695554762, 2246110022, 2378746131, 2889320799, 4181707719

Offset: 1

Author

Amiram Eldar, Feb 09 2020

Keywords

• nonn

Comments

The corresponding common values A103224(k) = A103224(k+1) are 8, 8, 288, 640, 7200, 139392, 3744000, 5760000, ...

Examples

			4 is a term since norm(phi(4)) = norm(phi(5)) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..37

Crossrefs

Cf. A001274, A103222, A103223, A103224, A287055, A293184, A326403.

Programs

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]]; Select[Range[10^3], Abs[phi[#]]^2 == Abs[phi[# + 1]]^2 &] (* after T. D. Noe at A103222 *)