|
%I #15 Nov 15 2021 11:10:04
%S 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,
%T 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,
%U 0,1,0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0
%N a(n) is the number of iterations that n requires to reach a fixed point under the map x -> A348158(x).
%C a(n) first differs from 1-A000035(n) at n = 63.
%C The number of iterations is finite for all n since A348158(n) <= n.
%C The fixed points are terms of A326835, so a(n) = 0 if and only if n is a term of A326835.
%H Amiram Eldar, <a href="/A348213/b348213.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 0 since 1 is in A326835.
%e a(2) = 1 since there is one iteration of the map x -> A348158(x) starting from 2: 2 -> 1.
%e a(64) = 2 since there are 2 iterations of the map x -> A348158(x) starting from 64: 64 -> 63 -> 57.
%t f[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]; a[n_] := -2 + Length @ FixedPointList[f, n]; Array[a, 100]
%o (Python)
%o from sympy import totient, divisors
%o def A348213(n):
%o c, k = 0, n
%o m = sum(set(map(totient,divisors(k,generator=True))))
%o while m != k:
%o k = m
%o m = sum(set(map(totient,divisors(k,generator=True))))
%o c += 1
%o return c # _Chai Wah Wu_, Nov 15 2021
%Y Cf. A000035, A003434, A326835, A348158.
%K nonn
%O 1,64
%A _Amiram Eldar_, Oct 07 2021
|
