A380342 a(n) = phi(1 + phi(8 + phi(27 + ... phi(n^3)))).

1, 4, 12, 12, 36, 40, 36, 72, 156, 112, 48, 112, 110, 116, 72, 72, 36, 88, 72, 88, 116, 88, 88, 36, 48, 72, 88, 96, 88, 88, 88, 116, 116, 72, 36, 88, 116, 116, 36, 88, 116, 112, 48, 72, 112, 116, 116, 116, 116, 116, 88, 88, 72, 88, 116, 116, 88, 72, 88, 88, 88, 36, 116

Offset: 1

Author

Michel Marcus, Jan 22 2025

Keywords

• nonn

Comments

a(n) is either 1, 4, 12, 36, 40, 48, 72, 88, 96, 110, 112, 116, or 156 (see Vela and Wolird). - Chai Wah Wu, Jan 22 2025

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo Xausa)
• Luis Palacios Vela and Christian Wolird, The Forestry of Adversarial Totient Iterations, arXiv:2501.10616 [math.NT], 2025.

Crossrefs

Cf. A000010, A380340, A380341, A380354, A380414, A380415.

Programs

Mathematica

A380342[n_] := Fold[EulerPhi[#2 + #] &, 0, Range[n, 1, -1]^3];
Array[A380342, 100] (* Paolo Xausa, Jan 22 2025 *)

PARI

a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(x+k^3)); x;

Python

from functools import reduce
from sympy import totient
def A380342(n): return reduce(lambda x,y:totient(x)+y,(m**3 for m in range(n,-1,-1))) # Chai Wah Wu, Jan 22 2025