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

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

Offset: 0

Author

Chai Wah Wu, Sep 05 2023

Keywords

• nonn
• hard
• more

Comments

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

Crossrefs

Cf. A000005, A365399.

Programs

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