Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #29 May 09 2022 09:23:36
%S 1,11,13,17,19,31,41,61,71,101,103,107,109,113,121,127,131,137,139,
%T 143,149,151,157,163,167,169,173,179,181,187,191,193,197,199,211,221,
%U 241,251,271,281,311,313,317,331,341,361,401,419,421,431,451,461,491,521
%N Numbers k such that every divisor of k contains the digit 1.
%C First composite term is 121. All powers of 11 are in the sequence. - _Alonso del Arte_, Sep 29 2013
%H Reinhard Zumkeller, <a href="/A062634/b062634.txt">Table of n, a(n) for n = 1..10000</a>
%e 143 has divisors 1, 11, 13 and 143, all of which contain the digit 1.
%p q:= n-> andmap(x-> 1 in convert(x, base, 10), numtheory[divisors](n)):
%p select(q, [$1..1000])[]; # _Alois P. Heinz_, May 09 2022
%t 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 (Haskell)
%o a062634 n = a062634_list !! (n-1)
%o a062634_list = filter
%o (and . map ((elem '1') . show) . a027750_row) a011531_list
%o -- _Reinhard Zumkeller_, Feb 05 2012
%o (PARI) isok(m) = fordiv(m, d, if (! #select(x->(x==1), digits(d)), return(0))); return(1); \\ _Michel Marcus_, May 09 2022
%Y Cf. A027750, subsequence of A011531; A206159 and A208270 are subsequences.
%Y Cf. A001020 (powers of 11).
%K nonn,base,easy
%O 1,2
%A _Erich Friedman_, Jul 04 2001
%E Offset corrected by _Reinhard Zumkeller_, Feb 05 2012