A103225 Number of Gaussian integers z with abs(z) < n and gcd(n,z)=1.

1, 4, 24, 24, 44, 48, 144, 96, 224, 96, 372, 192, 444, 304, 404, 392, 792, 448, 1124, 408, 1200, 752, 1648, 808, 1240, 896, 2036, 1200, 2440, 800, 2996, 1600, 3008, 1592, 2404, 1808, 4056, 2256, 3616, 1600, 4992, 2400, 5784, 3008, 3604, 3304, 6916, 3224, 7376

Offset

1,2

Comments

This sequence is much like the usual totient function. That is, it gives the number of Gaussian integers that are relatively prime to n and whose modulus is less than n. When n is a Gaussian prime, A002145, then a(n) = A051132(n)-1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..200 from T. D. Noe)

Example

a(2)=4 because 1, -1, i and -i are relatively prime to 2 and have modulus less than 2.

Mathematica

Table[cnt=0; Do[z=a+ b*I; If[Abs[z]<n && GCD[n, z]==1, cnt++ ], {a, -n+1, n-1}, {b, -n+1, n-1}]; cnt, {n, 60}]

Crossrefs

Cf. A002145, A051132, A103222, A103223, A103224.

Sequence in context: A233149 A169688 A222595 * A303333 A324517 A370493

Adjacent sequences: A103222 A103223 A103224 * A103226 A103227 A103228

Keyword

nice,nonn

Author

T. D. Noe, Jan 26 2005

Status

approved