login
a(n) = A365742(10^n).
1

%I #18 Oct 18 2023 10:06:21

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

%N a(n) = A365742(10^n).

%H R. Baker and G. Harman, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8342.pdf">Shifted primes without large prime factors</a>, Acta Arithmetica 83 (1998), pp. 331-361.

%H Paul Pollack, Carl Pomerance, and Enrique Treviño, <a href="https://math.dartmouth.edu/~carlp/MonotonePhi.pdf">Sets of monotonicity for Euler's totient function</a>, preprint. See M0(n).

%H Paul Pollack, Carl Pomerance, and Enrique Treviño, <a href="https://doi.org/10.1007/s11139-012-9386-6">Sets of monotonicity for Euler's totient function</a>, Ramanujan J. 30 (2013), no. 3, 379-398.

%H Terence Tao, <a href="https://arxiv.org/abs/2309.02325">Monotone non-decreasing sequences of the Euler totient function</a>, arXiv:2309.02325 [math.NT], 2023.

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

%o (Python)

%o from collections import Counter

%o from sympy import totient

%o def A365748(n): return max(Counter(totient(i) for i in range(1,10**n+1)).values())

%Y Cf. A000010, A000720.

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

%K nonn,hard,more

%O 0,2

%A _Chai Wah Wu_, Sep 17 2023