A045813 Base-4 numbers whose list of divisors (in base 4) contains each digit 0-3 the same number of times.

320, 20132, 21320, 22033, 23201, 30023, 30203, 30320, 32320, 321202, 1002233, 1002323, 1022033, 1022303, 1032023, 1200323, 1202033, 1202303, 1230203, 1232003, 1300223, 1302023, 1302203, 1320023, 2003201, 2003213, 2003231, 2003312, 2012303, 2013032, 2013212

Offset: 1

Author

Naohiro Nomoto

Keywords

• nonn
• base
• easy

Examples

			Divisors of 32320 are {1, 2, 10, 13, 20, 32, 101, 130, 202, 320, 1010, 1313, 2020, 3232, 13130, 32320} in base 4; each digit appears 12 times.
		

Links

• Naohiro Nomoto, In the list of divisors of n, ...

Crossrefs

Cf. A038564, A038565, A045814.

Programs

Python

from sympy import divisors
from collections import Counter
from sympy.ntheory import digits
def b4(n): return int("".join(map(str, digits(n, 4)[1:])))
def ok(n):
    c = Counter()
    for d in divisors(n, generator=True): c.update(digits(d, 4)[1:])
    return c[0] == c[1] == c[2] == c[3]
print([b4(k) for k in range(1, 4**7) if ok(k)]) # Michael S. Branicky, Nov 12 2022