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

1, 11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 211, 221, 241, 251, 271, 281, 311, 313, 317, 331, 341, 361, 401, 419, 421, 431, 451, 461, 491, 521

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• nonn
• base
• easy

Comments

First composite term is 121. All powers of 11 are in the sequence. - Alonso del Arte, Sep 29 2013

Examples

			143 has divisors 1, 11, 13 and 143, all of which contain the digit 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027750, subsequence of A011531; A206159 and A208270 are subsequences.

Cf. A001020 (powers of 11).

Programs

Haskell

a062634 n = a062634_list !! (n-1)
a062634_list = filter
   (and . map ((elem '1') . show) . a027750_row) a011531_list
-- Reinhard Zumkeller, Feb 05 2012

Maple

q:= n-> andmap(x-> 1 in convert(x, base, 10), numtheory[divisors](n)):
select(q, [$1..1000])[];  # Alois P. Heinz, May 09 2022

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 525], fQ[#, 1] &] (* Robert G. Wilson v, Jun 11 2014 *)

PARI

isok(m) = fordiv(m, d, if (! #select(x->(x==1), digits(d)), return(0))); return(1); \\ Michel Marcus, May 09 2022

Extensions

Offset corrected by Reinhard Zumkeller, Feb 05 2012