A334725 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.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..90.

L. Alaoglu and P. Erdős, A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), 881-882.

Example

Table begins:
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
...
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.

Mathematica

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

Crossrefs

For other versions, see A032452, A334523.

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

Sequence in context: A375478 A073932 A082404 * A120885 A234575 A294733

Adjacent sequences: A334722 A334723 A334724 * A334726 A334727 A334728

Keyword

nonn,tabf

Author

Amiram Eldar, May 09 2020

Status

approved