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

1,1

Links

Table of n, a(n) for n=1..31.

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

Example

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.

Prog

(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

Crossrefs

Cf. A038564, A038565, A045814.

Sequence in context: A055863 A168636 A264140 * A121011 A264063 A174778

Adjacent sequences: A045810 A045811 A045812 * A045814 A045815 A045816

Keyword

nonn,base,easy

Author

Naohiro Nomoto

Status

approved