A348264 - OEIS

%I #14 Jul 19 2022 22:32:33

%S 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,

%T 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,

%U 0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,2,0,1,0

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

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

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

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

%H Amiram Eldar, <a href="/A348264/b348264.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 0 since 1 is in A348004.

%e a(2) = 1 since there is one iteration of the map x -> A348173(x) starting from 2: 2 -> 1.

%e a(84) = 2 since there are 2 iterations of the map x -> A348173(x) starting from 84: 84 -> 78 -> 39.

%t 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]

%Y Cf. A047994, A011765, A348004, A348173.

%K nonn

%O 1,84

%A _Amiram Eldar_, Oct 09 2021