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%I #20 Nov 12 2022 11:33:34
%S 320,20132,21320,22033,23201,30023,30203,30320,32320,321202,1002233,
%T 1002323,1022033,1022303,1032023,1200323,1202033,1202303,1230203,
%U 1232003,1300223,1302023,1302203,1320023,2003201,2003213,2003231,2003312,2012303,2013032,2013212
%N Base-4 numbers whose list of divisors (in base 4) contains each digit 0-3 the same number of times.
%H Naohiro Nomoto, <a href="https://web.archive.org/web/20000916012426/http://www.geocities.co.jp/Technopolis/1793/09digit.htm">In the list of divisors of n, ...</a>
%e 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.
%o (Python)
%o from sympy import divisors
%o from collections import Counter
%o from sympy.ntheory import digits
%o def b4(n): return int("".join(map(str, digits(n, 4)[1:])))
%o def ok(n):
%o c = Counter()
%o for d in divisors(n, generator=True): c.update(digits(d, 4)[1:])
%o return c[0] == c[1] == c[2] == c[3]
%o print([b4(k) for k in range(1, 4**7) if ok(k)]) # _Michael S. Branicky_, Nov 12 2022
%Y Cf. A038564, A038565, A045814.
%K nonn,base,easy
%O 1,1
%A _Naohiro Nomoto_
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