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A045813
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Base-4 numbers whose list of divisors (in base 4) contains each digit 0-3 the same number of times.
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1
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..31.
Naohiro Nomoto, In the list of divisors of n, ...
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A038564, A038565, A045814.
Sequence in context: A055863 A168636 A264140 * A121011 A264063 A174778
Adjacent sequences: A045810 A045811 A045812 * A045814 A045815 A045816
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KEYWORD
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nonn,base,easy
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AUTHOR
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Naohiro Nomoto
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STATUS
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approved
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