A357429 Numbers whose digit representation in base 3 is equal to the digit representation in base 3 of the initial terms of their sets of divisors in increasing order.

1, 48, 50, 333, 438, 448, 734217, 6561081

Offset: 1

Author

Michel Marcus, Sep 28 2022

Keywords

• nonn
• base
• more

Examples

			In base 3, 48 is 1210 and its first divisors are 1, 2 and 3, that is, 1, 2 and 10.
		

Crossrefs

Cf. A175252 (base 10), A357428 (base 2).

Programs

PARI

isok(k) = my(s=[]); fordiv(k, d, s=concat(s, digits(d, 3)); if (fromdigits(s, 3)==k, return(1)); if (fromdigits(s, 3)> k, return(0)));

Python

from sympy import divisors
from sympy.ntheory import digits
def ok(n):
    target, s = "".join(map(str, digits(n, 3)[1:])), ""
    if target[0] != "1": return False
    for d in divisors(n):
        s += "".join(map(str, digits(d, 3)[1:]))
        if len(s) >= len(target): return s == target
        elif not target.startswith(s): return False
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Oct 01 2022