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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A351491 A107701 A293812 * A011176 A154542 A360459

Adjacent sequences: A380350 A380351 A380352 * A380355 A380356 A380357

Keyword

nonn,new

Author

Paolo Xausa, Jan 22 2025

Status

approved