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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A262503 A263082 A043343 * A066080 A319270 A071707

Adjacent sequences: A380411 A380412 A380414 * A380416 A380417 A380418

Keyword

nonn,new

Author

Paolo Xausa, Jan 24 2025

Status

approved