A365742 -id:A365742 - cp's OEIS frontend

A365748 a(n) = A365742(10^n).

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

Offset: 0

Chai Wah Wu, Sep 17 2023

R. Baker and G. Harman, Shifted primes without large prime factors, Acta Arithmetica 83 (1998), pp. 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.

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

from collections import Counter
from sympy import totient
def A365748(n): return max(Counter(totient(i) for i in range(1,10**n+1)).values())

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

A365741 a(n) = A365740(10^n).

Original entry on oeis.org

1, 5, 31, 189, 1261, 9595, 77681, 654249, 5650472

Offset: 0

Chai Wah Wu, Sep 17 2023

Pollack et al. listed a(4)-a(6).

Paul Pollack, Carl Pomerance and Enrique Treviño, Sets of monotonicity for Euler's totient function, preprint. See M2(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.

Cf. A000010, A000720.

Cf. A365398, A365399, A365400, A365474, A365737, A365740, A365742, A061070.

from bisect import bisect
from sympy import totient
def A365741(n):
    k = 10**n
    plist = tuple(totient(i) for i in range(1,k+1) if not isprime(i))
    m = len(plist)
    qlist, c = [0]*(m+1), 0
    for i in range(m):
        qlist[a:=bisect(qlist,plist[i],lo=1,hi=c+1,key=lambda x:plist[x])]=i
        c = max(c,a)
    return c

cp's OEIS Frontend

A365748 a(n) = A365742(10^n).

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