A348264 a(n) is the number of iterations that n requires to reach a fixed point under the map x -> A348173(x).

0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0

Offset: 1

Author

Amiram Eldar, Oct 09 2021

Keywords

• nonn

Comments

a(n) first differs from A011765(n+2) at n = 84.

The fixed points are terms of A348004, so a(n) = 0 if and only if n is a term of A348004.

Conjecture: essentially partial sums of A219977 (verified for n <= 5000).

Examples

			a(1) = 0 since 1 is in A348004.
a(2) = 1 since there is one iteration of the map x -> A348173(x) starting from 2: 2 -> 1.
a(84) = 2 since there are 2 iterations of the map x -> A348173(x) starting from 84: 84 -> 78 -> 39.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A047994, A011765, A348004, A348173.

Programs

Mathematica

f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; a[n_] := -2 + Length@ FixedPointList[s, n]; Array[a, 100]