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A221697 Numbers whose largest digit of all divisors is 2.

%I A221697 #33 Aug 03 2022 10:48:34
%S A221697 2,22,121,202,211,1021,1201,2011,2111,2221,2222,10201,10211,12011,
%T A221697 12101,12211,12221,20011,20021,20101,20201,20222,21001,21011,21101,
%U A221697 21121,21211,21221,22111,22121,101021,101221,102001,102101,102121,110221,111121,111211,111221,112111,112121
%N A221697 Numbers whose largest digit of all divisors is 2.
%C A221697 Also numbers k such that the largest digit of the concatenation of all the divisors (A037278) of k is 2.
%C A221697 Numbers k such that A209928(k) = 2.
%C A221697 Union of A221698 and A106100.
%H A221697 Michael S. Branicky, <a href="/A221697/b221697.txt">Table of n, a(n) for n = 1..10000</a>
%e A221697 10201 is a term because the largest digit of all the divisors of 10201 (1, 101, 10201) is 2.
%p A221697 isA221697 := proc(n)
%p A221697       local dgs,d;
%p A221697       dgs := {} ;
%p A221697     for d in numtheory[divisors](n) do
%p A221697         dgs := dgs union convert(convert(d,base,10),set) ;
%p A221697     end do:
%p A221697     if max(op(dgs)) = 2 then
%p A221697         true;
%p A221697     else
%p A221697         false;
%p A221697     end if;
%p A221697 end proc:
%p A221697 for n from 2 to 112121 do
%p A221697     if isA221697(n) then
%p A221697         printf("%d,",n) ;
%p A221697     end if;
%p A221697 end do: # _R. J. Mathar_, Jan 30 2013
%t A221697 Select[Range[115000],Max[Flatten[IntegerDigits/@Divisors[#]]]==2&] (* _Harvey P. Dale_, Dec 15 2014 *)
%o A221697 (Python)
%o A221697 from sympy import divisors
%o A221697 def ok(n): return '2' == max("".join(map(str, divisors(n))))
%o A221697 print([m for m in range(1, 112122) if ok(m)]) # _Michael S. Branicky_, Feb 22 2021
%o A221697 (Python)
%o A221697 from sympy import isprime, divisors
%o A221697 from itertools import count, islice, product
%o A221697 def agen(): # generator of terms
%o A221697     yield 2
%o A221697     for d in count(2):
%o A221697         for f in "12":
%o A221697             for mid in product("012", repeat=d-2):
%o A221697                 for e in "12": # ending in zero has 5 as divisor
%o A221697                     s = f+"".join(mid)+e
%o A221697                     t = int(s)
%o A221697                     if "2" in s and isprime(t): yield t; continue
%o A221697                     if "2" == max("".join(map(str, divisors(t)))): yield t
%o A221697 print(list(islice(agen(), 50))) # _Michael S. Branicky_, Aug 03 2022
%Y A221697 Cf. A037278, A106100, A209928 (largest digit of all divisors of n), A221698.
%K A221697 nonn,base
%O A221697 1,1
%A A221697 _Jaroslav Krizek_, Jan 22 2013, corrected Jan 29 2013