A365738 a(n) = A365737(10^n).

1, 3, 12, 32, 92, 292, 995, 3029, 9651, 31817

Offset: 0

Author

Chai Wah Wu, Sep 17 2023

Keywords

• nonn
• hard
• more

Links

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

Cf. A000010, A000720.

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

Programs

Python

from bisect import bisect
from sympy import totient
def A365738(n):
    k = 10**n
    plist, qlist, c = tuple(-totient(i) for i in range(1,k+1)), [0]*(k+1), 0
    for i in range(k):
        qlist[a:=bisect(qlist,plist[i],lo=1,hi=c+1,key=lambda x:plist[x])]=i
        c = max(c,a)
    return c

Extensions

a(9) from Chai Wah Wu, Oct 13 2023