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A062634 Numbers k such that every divisor of k contains the digit 1.

%I A062634 #29 May 09 2022 09:23:36
%S A062634 1,11,13,17,19,31,41,61,71,101,103,107,109,113,121,127,131,137,139,
%T A062634 143,149,151,157,163,167,169,173,179,181,187,191,193,197,199,211,221,
%U A062634 241,251,271,281,311,313,317,331,341,361,401,419,421,431,451,461,491,521
%N A062634 Numbers k such that every divisor of k contains the digit 1.
%C A062634 First composite term is 121. All powers of 11 are in the sequence. - _Alonso del Arte_, Sep 29 2013
%H A062634 Reinhard Zumkeller, <a href="/A062634/b062634.txt">Table of n, a(n) for n = 1..10000</a>
%e A062634 143 has divisors 1, 11, 13 and 143, all of which contain the digit 1.
%p A062634 q:= n-> andmap(x-> 1 in convert(x, base, 10), numtheory[divisors](n)):
%p A062634 select(q, [$1..1000])[];  # _Alois P. Heinz_, May 09 2022
%t A062634 fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 525], fQ[#, 1] &] (* _Robert G. Wilson v_, Jun 11 2014 *)
%o A062634 (Haskell)
%o A062634 a062634 n = a062634_list !! (n-1)
%o A062634 a062634_list = filter
%o A062634    (and . map ((elem '1') . show) . a027750_row) a011531_list
%o A062634 -- _Reinhard Zumkeller_, Feb 05 2012
%o A062634 (PARI) isok(m) = fordiv(m, d, if (! #select(x->(x==1), digits(d)), return(0))); return(1); \\ _Michel Marcus_, May 09 2022
%Y A062634 Cf. A027750, subsequence of A011531; A206159 and A208270 are subsequences.
%Y A062634 Cf. A001020 (powers of 11).
%K A062634 nonn,base,easy
%O A062634 1,2
%A A062634 _Erich Friedman_, Jul 04 2001
%E A062634 Offset corrected by _Reinhard Zumkeller_, Feb 05 2012