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

1,4

Comments

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

Links

Table of n, a(n) for n=1..90.

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A331292 A331293 A335379 * A342121 A258764 A109083

Adjacent sequences: A358058 A358059 A358060 * A358062 A358063 A358064

Keyword

nonn

Author

Ctibor O. Zizka, Oct 28 2022

Status

approved