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

1,2

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.

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

Cf. A000010, A000720.

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

Sequence in context: A307726 A235123 A242768 * A064557 A365737 A023967

Adjacent sequences: A365739 A365740 A365741 * A365743 A365744 A365745

Keyword

nonn

Author

Chai Wah Wu, Sep 17 2023

Status

approved