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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A325948 A216801 A083833 * A292452 A292732 A206418

Adjacent sequences: A221694 A221695 A221696 * A221698 A221699 A221700

Keyword

nonn,base

Author

Jaroslav Krizek, Jan 22 2013, corrected Jan 29 2013

Status

approved