cp's OEIS Frontend

A365742 Length of the largest subset of 1,...,n on which the Euler totient function phi A000010 is constant.

%I A365742 #22 Sep 18 2023 14:09:24
%S A365742 1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,
%T A365742 5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A365742 6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10
%N A365742 Length of the largest subset of 1,...,n on which the Euler totient function phi A000010 is constant.
%H A365742 Chai Wah Wu, <a href="/A365742/b365742.txt">Table of n, a(n) for n = 1..10000</a>
%H A365742 R. C. Baker and G. Harman, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8342.pdf">Shifted primes without large prime factors</a>, Acta Arith. 83 (1998), no. 4, 331-361.
%H A365742 Paul Erdős, <a href="https://static.renyi.hu/~p_erdos/1935-08.pdf">On the normal number of prime factors of p - 1 and some related problems concerning Euler’s phi-function</a>, Quart J. Math 6 (1935), 205-213.
%H A365742 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 A365742 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 A365742 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 A365742 Pollack et al. showed that A365737(n)-a(n) > n^0.18 for large n.
%o A365742 (Python)
%o A365742 from collections import Counter
%o A365742 from sympy import totient
%o A365742 def A365742(n): return max(Counter(totient(i) for i in range(1,n+1)).values())
%Y A365742 Cf. A000010, A000720.
%Y A365742 Cf. A365398, A365399, A365400, A365474, A365737, A365738, A365740, A365741, A061070.
%K A365742 nonn
%O A365742 1,2
%A A365742 _Chai Wah Wu_, Sep 17 2023