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A209931 Numbers k such that smallest digit of all divisors of k is 1.

%I A209931 #21 Jul 03 2025 02:37:24
%S A209931 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,
%T A209931 29,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,51,52,53,54,
%U A209931 55,56,57,58,59,61,62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,78,79,81,82,83,84,85,86,87,88,89,91,92,93,94,95,96,97,98,99,111
%N A209931 Numbers k such that smallest digit of all divisors of k is 1.
%C A209931 Also numbers k such that smallest digit of concatenation of all divisors of k (A037278 or A176558) is 1.
%C A209931 Sequence is not the same as A052382, first deviation is at a(173): A052382(173) = 212, a(173) = 213. [Corrected by _Michael S. Branicky_, Jul 01 2025.]
%C A209931 Sequence is not the same as A067251, first deviation is at a(91): A067251 (91) = 101, a(91) = 111.
%C A209931 Complement of A209932.
%H A209931 Michael S. Branicky, <a href="/A209931/b209931.txt">Table of n, a(n) for n = 1..10000</a>
%e A209931 Number 24 is in sequence because smallest digit of all divisors of 24 (1, 2, 4, 8, 3, 6, 12, 24) is 1.
%p A209931 isA209931 := proc(n)
%p A209931     digsdiv := {} ;
%p A209931     for d in numtheory[divisors](n) do
%p A209931         dgs := convert(convert(d,base,10),set) ;
%p A209931         digsdiv := digsdiv union dgs ;
%p A209931     end do:
%p A209931     if 0 in digsdiv then
%p A209931         false;
%p A209931     else
%p A209931         true ;
%p A209931     end if;
%p A209931 end proc:
%p A209931 A209931 := proc(n)
%p A209931     option remember;
%p A209931     if n =1 then
%p A209931         1;
%p A209931     else
%p A209931         for a from procname(n-1)+1 do
%p A209931             if isA209931(a) then
%p A209931                 return a;
%p A209931             end if;
%p A209931         end do;
%p A209931     end if;
%p A209931 end proc:
%p A209931 seq(A209931(n),n=1..120) ;# _R. J. Mathar_, Dec 28 2023
%t A209931 Select[Range[100], Min[IntegerDigits[Divisors[#]]] == 1 &] (* _Paolo Xausa_, Jul 03 2025 *)
%o A209931 (Python)
%o A209931 from sympy import divisors
%o A209931 def ok(n): return all('0' not in str(d) for d in divisors(n, generator=True))
%o A209931 print([k for k in range(1, 112) if ok(k)]) # _Michael S. Branicky_, Jul 01 2025
%Y A209931 Cf. A052382, A067251, A209929 (smallest digit of all divisors of n).
%K A209931 nonn,base
%O A209931 1,2
%A A209931 _Jaroslav Krizek_, Mar 20 2012