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A206159 Numbers needing at most two digits to write all positive divisors in decimal representation.

%I A206159 #51 May 04 2022 00:28:53
%S A206159 1,2,3,5,7,11,13,17,19,22,31,33,41,55,61,71,77,101,113,121,131,151,
%T A206159 181,191,199,211,311,313,331,661,811,881,911,919,991,1111,1117,1151,
%U A206159 1171,1181,1511,1777,1811,1999,2111,2221,3313,3331,4111,4441,6661,7177,7717,8111,9199,10111,11113
%N A206159 Numbers needing at most two digits to write all positive divisors in decimal representation.
%C A206159 The terms of A203897 having all divisors in A020449 (in particular, the first 1022 terms) are a subsequence. - _M. F. Hasler_, May 02 2022
%C A206159 Since 1 and the term itself are divisors, one must only check repdigits and those containing only 1 and another digit. - _Michael S. Branicky_, May 02 2022
%H A206159 Michael S. Branicky, <a href="/A206159/b206159.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from M. F. Hasler)
%F A206159 A095048(a(n)) <= 2.
%t A206159 Select[Range[12000],Length[Union[Flatten[IntegerDigits/@Divisors[#]]]]<3&] (* _Harvey P. Dale_, May 03 2022 *)
%o A206159 (Python)
%o A206159 from sympy import divisors
%o A206159 def ok(n):
%o A206159     digits_used = set()
%o A206159     for d in divisors(n, generator=True):
%o A206159         digits_used |= set(str(d))
%o A206159         if len(digits_used) > 2: return False
%o A206159     return True
%o A206159 print([k for k in range(1, 9000) if ok(k)]) # _Michael S. Branicky_, May 02 2022
%o A206159 (PARI) select( {is_A206159(n)=#Set(concat([digits(d)|d<-divisors(n)]))<3}, [1..10^4]) \\ _M. F. Hasler_, May 02 2022
%Y A206159 Cf. A027750, A031955, A011531, A106101, A004022, A062634.
%Y A206159 Cf. A203897 (an "almost subsequence"), A020449 (primes with only digits 0 & 1), A095048 (number of distinct digits in divisors(n)).
%K A206159 nonn,base
%O A206159 1,2
%A A206159 _Reinhard Zumkeller_, Feb 05 2012
%E A206159 Terms corrected by _Harvey P. Dale_, May 02 2022
%E A206159 Edited by _N. J. A. Sloane_, May 02 2022