A092912 Numbers k all of whose divisors contain only digits that occur at least once in k.

1, 11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 211, 241, 251, 271, 281, 311, 313, 317, 331, 341, 401, 419, 421, 431, 451, 461, 491, 521, 541, 571

Offset

1,2

Comments

All primes containing the digit 1 are terms.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

131 is a term. 143 is also a term with divisors 1,11,13,143.

Maple

isA092912 := proc(n) local digs, divs, d, i, j ; digs := convert(n, base, 10) ; divs := numtheory[divisors](n) ; for i from 1 to nops(divs) do d := convert(op(i, divs), base, 10) ; for j in d do if not j in digs then RETURN(false) ; fi ; od ; od ; RETURN(true) ; end: for n from 1 to 700 do if isA092912(n) then printf("%d, ", n) ; fi ; od ; # R. J. Mathar, Jul 26 2007

Mathematica

Do[a = IntegerDigits[n]; b = Union @@ IntegerDigits[Divisors[n]]; If[Intersection[a, b] == b, Print[n]], {n, 1, 200}] (* Ryan Propper, Jul 19 2005 *)

Prog

(PARI) is_A092912(n)=!setminus(Set(concat(apply(digits, divisors(n)))), Set(digits(n))) \\ M. F. Hasler, Mar 09 2014

Crossrefs

Cf. A062634, A092911.

Sequence in context: A155071 A003626 A154981 * A092911 A062634 A239058

Adjacent sequences: A092909 A092910 A092911 * A092913 A092914 A092915

Keyword

base,nonn

Author

Amarnath Murthy, Mar 14 2004

Extensions

Corrected and extended by Ryan Propper, Jul 19 2005

More terms from R. J. Mathar, Jul 26 2007

Status

approved