A365485 a(n) = A365399(10^n).

1, 7, 39, 298, 2615, 23438, 225682, 2229674, 21903726

Offset

0,2

Comments

a(n)/10^n appears to be decreasing. Conjecture: a(n)/10^n converges to a nonzero value.

Links

Table of n, a(n) for n=0..8.

Prog

(Python)
from bisect import bisect
from sympy import divisor_count
def A365485(n):
    m = 10**n
    plist, qlist, c = tuple(divisor_count(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. A000005, A365399.

Sequence in context: A139173 A219437 A219138 * A138417 A207154 A203111

Adjacent sequences: A365482 A365483 A365484 * A365486 A365487 A365488

Keyword

nonn,hard,more

Author

Chai Wah Wu, Sep 05 2023

Status

approved