A038564 Numbers whose list of divisors includes each digit 1-9 equally often.

54023, 54203, 55868, 500407, 556744, 769858, 1187666, 1566986, 1875098, 3545924, 5594156, 5733406, 5849014, 5908304, 6100594, 6712006, 7605544, 9106868, 9580654, 10909864, 23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657

Offset: 1

Author

Naohiro Nomoto

Keywords

• nonn
• base
• easy

Examples

			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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A038565.

Programs

Mathematica

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 *)

Python

from sympy import divisors
from collections import Counter
def ok(n):
    c = Counter()
    for d in divisors(n, generator=True): c.update(str(d))
    return len(set([c[i] for i in "123456789"])) == 1
print([k for k in range(1, 60000) if ok(k)]) # Michael S. Branicky, Nov 13 2022

Extensions

More terms from Sascha Kurz, Oct 18 2001

a(26) and beyond from Michael S. Branicky, Nov 13 2022