login
Numbers whose list of divisors includes each digit 1-9 equally often.
16

%I #16 Dec 20 2022 14:38:38

%S 54023,54203,55868,500407,556744,769858,1187666,1566986,1875098,

%T 3545924,5594156,5733406,5849014,5908304,6100594,6712006,7605544,

%U 9106868,9580654,10909864,23456789,23458679,23459687,23465789,23465987,23469587,23475869,23478569,23489657

%N Numbers whose list of divisors includes each digit 1-9 equally often.

%H Michael S. Branicky, <a href="/A038564/b038564.txt">Table of n, a(n) for n = 1..10000</a>

%e 55868 is a term because, among its divisors (which are 1, 2, 4, 13967, 27934, 55868), each digit from 1 through 9 occurs exactly twice.

%t ld9Q[n_]:=Module[{d=DeleteCases[Sort[Flatten[IntegerDigits/@Divisors[ n]]],0]},Length[ Intersection[ d,Range[ 9]]] == 9&&Length[Union[ Length/@Split[ d]]]==1]; Select[ Range[ 235*10^5],ld9Q] (* _Harvey P. Dale_, Dec 20 2022 *)

%o (Python)

%o from sympy import divisors

%o from collections import Counter

%o def ok(n):

%o c = Counter()

%o for d in divisors(n, generator=True): c.update(str(d))

%o return len(set([c[i] for i in "123456789"])) == 1

%o print([k for k in range(1, 60000) if ok(k)]) # _Michael S. Branicky_, Nov 13 2022

%Y Cf. A038565.

%K nonn,base,easy

%O 1,1

%A _Naohiro Nomoto_

%E More terms from _Sascha Kurz_, Oct 18 2001

%E a(26) and beyond from _Michael S. Branicky_, Nov 13 2022