A237608 Number of n-digit numbers that are divisible by a square and have the same property if any number of rightmost digits is deleted.

3, 14, 61, 263, 1128, 4788, 20271, 85885, 364408, 1546394, 6563924, 27863816, 118286561

Offset

1,1

Comments

See A237607 for the numbers themselves and for more comments.

The ratio r(n) = a(n+1)/a(n) seems to converge to a constant value of about 4.245...

Links

Table of n, a(n) for n=1..13.

Stanislav Sykora, PARI/GP scripts for genetic threads

Example

One-digit numbers k with moebius(k)=0 are 4, 8 and 9. Hence a(1) = 3.

Prog

(PARI) \\ See the link (use GT_DivMod0 with "IsMoebiusZero" for the "property" argument).
(Python)
from sympy.ntheory.factor_ import core
def P(n): return core(n) < n
reach = {4, 8, 9}
for d in range(1, 10001):
    print(len(reach), end=", ")
    newreach = set()
    for q in reach:
        for digit in range(10):
            t = 10*q + digit
            if P(t):
                newreach.add(t)
    reach = newreach
# Michael S. Branicky, Jun 03 2026

Crossrefs

Cf. A237607.

Sequence in context: A024037 A281349 A307268 * A100295 A376894 A291025

Adjacent sequences: A237605 A237606 A237607 * A237609 A237610 A237611

Keyword

nonn,hard,more,base

Author

Stanislav Sykora, Feb 15 2014

Extensions

a(12)-a(13) from Lars Blomberg, Jan 02 2016

Status

approved