A103223 Imaginary part of the totient function phi(n) for Gaussian integers. See A103222 for the real part and A103224 for the norm.

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, 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, 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

Offset

1,4

Comments

Note that a(n)=0 when n is in A004614, the product of real Gaussian primes. It appears that all terms are nonnegative.

Links

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

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]]; Im[Table[phi[n], {n, 100}]]

Crossrefs

Cf. A103222, A103224.

Sequence in context: A379308 A214178 A117652 * A091399 A350951 A263527

Adjacent sequences: A103220 A103221 A103222 * A103224 A103225 A103226

Keyword

nonn

Author

T. D. Noe, Jan 26 2005

Status

approved