A380415 a(n) = phi(1 + phi(3 + phi(5 + ... + phi(2*n-1)))), where phi is Euler's totient function (A000010).

1, 2, 6, 12, 18, 22, 42, 42, 72, 20, 48, 18, 12, 108, 20, 42, 20, 42, 20, 36, 42, 42, 36, 36, 36, 42, 20, 42, 42, 36, 36, 42, 20, 48, 48, 18, 36, 36, 36, 36, 48, 48, 20, 48, 48, 36, 20, 48, 96, 20, 96, 36, 20, 20, 42, 36, 36, 20, 36, 36, 36, 20, 20, 36, 36, 20

Offset: 1

Author

Paolo Xausa, Jan 24 2025

Keywords

• nonn

Comments

Inspired by A380340, A380341 and A380342.

Conjecture 1: a(n) can be only 1, 2, 6, 12, 18, 20, 22, 36, 42, 48, 72, 96 or 108.

Conjecture 2: for n >= 320, a(n) = 20.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A005408, A380340, A380341, A380342, A380414.

Programs

Mathematica

A380415[n_] := Fold[EulerPhi[#2 + #] &, 0, Range[2*n - 1, 1, -2]];
Array[A380415, 100]

PARI

a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(2*k-1+x)); x; \\ Michel Marcus, Jan 24 2025

Python

from functools import reduce
from sympy import totient
def A380415(n): return totient(reduce(lambda x,y:totient(x)+y,range((n<<1)-1,0,-2))) # Chai Wah Wu, Jan 25 2025