login
A348213
a(n) is the number of iterations that n requires to reach a fixed point under the map x -> A348158(x).
4
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0
OFFSET
1,64
COMMENTS
a(n) first differs from 1-A000035(n) at n = 63.
The number of iterations is finite for all n since A348158(n) <= n.
The fixed points are terms of A326835, so a(n) = 0 if and only if n is a term of A326835.
LINKS
EXAMPLE
a(1) = 0 since 1 is in A326835.
a(2) = 1 since there is one iteration of the map x -> A348158(x) starting from 2: 2 -> 1.
a(64) = 2 since there are 2 iterations of the map x -> A348158(x) starting from 64: 64 -> 63 -> 57.
MATHEMATICA
f[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]; a[n_] := -2 + Length @ FixedPointList[f, n]; Array[a, 100]
PROG
(Python)
from sympy import totient, divisors
def A348213(n):
c, k = 0, n
m = sum(set(map(totient, divisors(k, generator=True))))
while m != k:
k = m
m = sum(set(map(totient, divisors(k, generator=True))))
c += 1
return c # Chai Wah Wu, Nov 15 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 07 2021
STATUS
approved