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
Examples
131 is a term. 143 is also a term with divisors 1,11,13,143.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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
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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 *) -
PARI
is_A092912(n)=!setminus(Set(concat(apply(digits,divisors(n)))),Set(digits(n))) \\ M. F. Hasler, Mar 09 2014
Extensions
Corrected and extended by Ryan Propper, Jul 19 2005
More terms from R. J. Mathar, Jul 26 2007
Comments