A365748 a(n) = A365742(10^n).

1, 3, 10, 30, 72, 247, 937, 2844, 9261, 30742

Offset: 0

Author

Chai Wah Wu, Sep 17 2023

Keywords

• nonn
• hard
• more

Links

• R. Baker and G. Harman, Shifted primes without large prime factors, Acta Arithmetica 83 (1998), pp. 331-361.
• Paul Pollack, Carl Pomerance, and Enrique Treviño, Sets of monotonicity for Euler's totient function, preprint. See M0(n).
• Paul Pollack, Carl Pomerance, and Enrique Treviño, Sets of monotonicity for Euler's totient function, Ramanujan J. 30 (2013), no. 3, 379-398.
• Terence Tao, Monotone non-decreasing sequences of the Euler totient function, arXiv:2309.02325 [math.NT], 2023.

Crossrefs

Cf. A000010, A000720.

Cf. A365398, A365399, A365400, A365474, A365737, A365738, A365740, A365741, A365742, A061070.

Programs

Python

from collections import Counter
from sympy import totient
def A365748(n): return max(Counter(totient(i) for i in range(1,10**n+1)).values())

Formula

Baker and Harman showed that a(n) >= 10^(0.7038n) for all large enough n. - Chai Wah Wu, Oct 17 2023