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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

(Haskell)
a062634 n = a062634_list !! (n-1)
a062634_list = filter
   (and . map ((elem '1') . show) . a027750_row) a011531_list
-- Reinhard Zumkeller, Feb 05 2012
(PARI) isok(m) = fordiv(m, d, if (! #select(x->(x==1), digits(d)), return(0))); return(1); \\ Michel Marcus, May 09 2022

Crossrefs

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

Cf. A001020 (powers of 11).

Sequence in context: A154981 A092912 A092911 * A239058 A208270 A106101

Adjacent sequences: A062631 A062632 A062633 * A062635 A062636 A062637

Keyword

nonn,base,easy

Author

Erich Friedman, Jul 04 2001

Extensions

Offset corrected by Reinhard Zumkeller, Feb 05 2012

Status

approved