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A062634 Numbers k such that every divisor of k contains the digit 1. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
First composite term is 121. All powers of 11 are in the sequence. - Alonso del Arte, Sep 29 2013
LINKS
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
KEYWORD
nonn,base,easy
AUTHOR
Erich Friedman, Jul 04 2001
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Feb 05 2012
STATUS
approved

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Last modified February 26 13:41 EST 2024. Contains 370352 sequences. (Running on oeis4.)