A221697 Numbers whose largest digit of all divisors is 2.

2, 22, 121, 202, 211, 1021, 1201, 2011, 2111, 2221, 2222, 10201, 10211, 12011, 12101, 12211, 12221, 20011, 20021, 20101, 20201, 20222, 21001, 21011, 21101, 21121, 21211, 21221, 22111, 22121, 101021, 101221, 102001, 102101, 102121, 110221, 111121, 111211, 111221, 112111, 112121

Offset: 1

Author

Jaroslav Krizek, Jan 22 2013, corrected Jan 29 2013

Keywords

• nonn
• base

Comments

Also numbers k such that the largest digit of the concatenation of all the divisors (A037278) of k is 2.

Numbers k such that A209928(k) = 2.

Union of A221698 and A106100.

Examples

			10201 is a term because the largest digit of all the divisors of 10201 (1, 101, 10201) is 2.
		

Links

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

Crossrefs

Cf. A037278, A106100, A209928 (largest digit of all divisors of n), A221698.

Programs

Maple

isA221697 := proc(n)
      local dgs,d;
      dgs := {} ;
    for d in numtheory[divisors](n) do
        dgs := dgs union convert(convert(d,base,10),set) ;
    end do:
    if max(op(dgs)) = 2 then
        true;
    else
        false;
    end if;
end proc:
for n from 2 to 112121 do
    if isA221697(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jan 30 2013

Mathematica

Select[Range[115000],Max[Flatten[IntegerDigits/@Divisors[#]]]==2&] (* Harvey P. Dale, Dec 15 2014 *)

Python

from sympy import divisors
def ok(n): return '2' == max("".join(map(str, divisors(n))))
print([m for m in range(1, 112122) if ok(m)]) # Michael S. Branicky, Feb 22 2021

Python

from sympy import isprime, divisors
from itertools import count, islice, product
def agen(): # generator of terms
    yield 2
    for d in count(2):
        for f in "12":
            for mid in product("012", repeat=d-2):
                for e in "12": # ending in zero has 5 as divisor
                    s = f+"".join(mid)+e
                    t = int(s)
                    if "2" in s and isprime(t): yield t; continue
                    if "2" == max("".join(map(str, divisors(t)))): yield t
print(list(islice(agen(), 50))) # Michael S. Branicky, Aug 03 2022