A365742 Length of the largest subset of 1,...,n on which the Euler totient function phi A000010 is constant.
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, 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, 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
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
- R. C. Baker and G. Harman, Shifted primes without large prime factors, Acta Arith. 83 (1998), no. 4, 331-361.
- Paul Erdős, On the normal number of prime factors of p - 1 and some related problems concerning Euler’s phi-function, Quart J. Math 6 (1935), 205-213.
- 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
Programs
-
Python
from collections import Counter from sympy import totient def A365742(n): return max(Counter(totient(i) for i in range(1,n+1)).values())
Formula
Pollack et al. showed that A365737(n)-a(n) > n^0.18 for large n.