A334725 - OEIS

%I #7 May 09 2020 18:03:09

%S 1,2,1,3,2,1,4,2,1,5,4,2,3,2,1,6,2,1,7,6,2,3,2,1,8,4,2,3,2,1,9,6,2,3,

%T 2,1,10,4,2,3,2,1,11,10,4,7,6,2,3,2,1,12,4,2,3,2,1,13,12,4,7,6,2,3,2,

%U 1,14,6,2,3,2,1,15,8,4,7,6,2,3,2,1,16,8,4,7,6,2,3,2,1

%N Irregular table read by row: the n-th row gives values of successively iterating phi, phi and sigma, starting with the initial value n, until the value 1 is reached. If 1 is never reached, row n contains n, -1.

%H L. Alaoglu and P. Erdős, <a href="http://dx.doi.org/10.1090/S0002-9904-1944-08257-8">A conjecture in elementary number theory</a>, Bull. Amer. Math. Soc. 50 (1944), 881-882.

%e Table begins:

%e 1

%e 2, 1

%e 3, 2, 1

%e 4, 2, 1

%e 5, 4, 2, 3, 2, 1

%e 6, 2, 1

%e 7, 6, 2, 3, 2, 1

%e 8, 4, 2, 3, 2, 1

%e ...

%e For n = 5, phi(5) = 4, phi(4) = 2, sigma(2) = 3, phi(3) = 2, and phi(2) = 1, therefore the 5th row is 5, 4, 2, 3, 2, 1.

%t f[n_, i_] := If[Mod[i, 3] == 0, DivisorSigma[1, n], EulerPhi[n]]; g[n_] := Module[{i = 1, k = n, s = {}}, While[AppendTo[s, k]; k > 1, k = f[k, i++]]; s]; Array[g, 16] // Flatten

%Y For other versions, see A032452, A334523.

%Y Cf. A000010 (phi), A000203 (sigma), A334685, A334686.

%K nonn,tabf

%O 1,2

%A _Amiram Eldar_, May 09 2020