A365474 a(n) = A365339(10^n).

1, 7, 34, 193, 1276, 9656, 78562, 664643, 5761519, 50847598

Offset

0,2

Comments

The Pollack et al. reference lists a(4)-a(7) and conjectures that A365339(n) = A000720(n)+64 for n >= 31957 which in turns implies the conjecture that a(n) = A006880(n)+64 for n >= 5.

Links

Table of n, a(n) for n=0..9.

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, pp. 379-398.

Terence Tao, Monotone non-decreasing sequences of the Euler totient function, arXiv:2309.02325 [math.NT], 2023.

Formula

a(n) = A006880(n)+64 for n >= 5 (conjectured).

Prog

(Python)
from bisect import bisect
from sympy import totient
def A365474(n):
    m = 10**n
    plist, qlist, c = tuple(totient(i) for i in range(1, m+1)), [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

Crossrefs

Cf. A000010, A000720, A006880, A365339.

Sequence in context: A027233 A117650 A370618 * A273221 A144038 A027842

Adjacent sequences: A365471 A365472 A365473 * A365475 A365476 A365477

Keyword

nonn,hard,more

Author

Chai Wah Wu, Sep 04 2023

Status

approved