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A365742 Length of the largest subset of 1,...,n on which the Euler totient function phi A000010 is constant. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
R. C. Baker and G. Harman, Shifted primes without large prime factors, Acta Arith. 83 (1998), no. 4, 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.
FORMULA
Pollack et al. showed that A365737(n)-a(n) > n^0.18 for large n.
PROG
(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())
CROSSREFS
Sequence in context: A307726 A235123 A242768 * A064557 A365737 A023967
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Sep 17 2023
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)