A358061 a(n) = phi(n) mod tau(n).

0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 3, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0

Offset: 1

Author

Ctibor O. Zizka, Oct 28 2022

Keywords

• nonn

Comments

a(n) > 0 for n in A015733, a(n) = 0 for n in A020491.

Examples

			For n = 4; a(4) = A000010(4) mod A000005(4) = 2 mod 3 = 2.
		

Crossrefs

Cf. A000005 (tau), A000010 (phi), A015733, A020491.

Programs

Mathematica

a[n_] := Mod[EulerPhi[n], DivisorSigma[0, n]]; Array[a, 100] (* Amiram Eldar, Oct 28 2022 *)

Python

from math import prod
from sympy import factorint
def A358061(n):
    f = factorint(n).items()
    d = prod(e+1 for p, e in f)
    return prod(pow(p,e-1,d)*((p-1)%d) for p, e in f) % d # Chai Wah Wu, Oct 29 2022

Formula

a(n) = A000010(n) mod A000005(n).