A380354 a(n) = phi(2 + phi(3 + phi(5 + ... + phi(prime(n))))), where phi is Euler totient function (A000010).

1, 2, 4, 6, 4, 8, 8, 12, 12, 16, 20, 20, 18, 40, 40, 16, 18, 18, 16, 72, 40, 16, 40, 18, 96, 96, 18, 64, 20, 40, 20, 48, 42, 40, 42, 20, 20, 40, 40, 20, 18, 20, 64, 64, 20, 40, 40, 40, 40, 20, 40, 20, 18, 64, 64, 40, 40, 20, 40, 20, 40, 64, 20, 40, 40, 20, 20, 64, 64, 64

Offset: 1

Author

Paolo Xausa, Jan 22 2025

Keywords

• nonn

Comments

Inspired by A380340, A380341 and A380342.

Conjecture 1: a(n) can be only 1, 2, 4, 6, 8, 12, 16, 20, 18, 40, 72, 96, 64, 48 or 42.

Conjecture 2: for n >= 187, a(n) can be only 20 or 64.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A380340, A380341, A380342, A380414, A380415.

Programs

Mathematica

A380354[n_] := Fold[EulerPhi[#2 + #] &, 0, Prime[Range[n, 1, -1]]];
Array[A380354, 100]

PARI

a(n) = my(x=0); forstep(k=n, 1, -1, x = eulerphi(prime(k)+x)); x; \\ Michel Marcus, Jan 22 2025

Python

from functools import reduce
from sympy import totient, primerange
def A380354(n): return totient(reduce(lambda x,y:totient(x)+y,tuple(reversed(tuple(primerange(prime(n)+1)))))) # Chai Wah Wu, Jan 23 2025