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A062679
Numbers such that every divisor (except 1, but including the number itself) contains the digit 9.
18
19, 29, 59, 79, 89, 97, 109, 139, 149, 179, 191, 193, 197, 199, 229, 239, 269, 293, 349, 359, 379, 389, 397, 409, 419, 439, 449, 479, 491, 499, 509, 569, 593, 599, 619, 659, 691, 709, 719, 739, 769, 797, 809, 829, 839, 859, 907, 911, 919, 929, 937, 941, 947
OFFSET
1,1
COMMENTS
Different from A106093. 1691 = 19 * 89 is the smallest term that is not in A106093. - Franklin T. Adams-Watters, Apr 30 2007
LINKS
EXAMPLE
7961 has divisors 19, 419 and 7961, all of which contain the digit 9.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1000], fQ[#, 9] &] (* Robert G. Wilson v, Jun 11 2014 *)
d9Q[n_]:=First[Union[DigitCount[#, 10, 9]&/@Rest[Divisors[n]]]]>0; Select[ Range[ 2, 1000], d9Q] (* Harvey P. Dale, Sep 12 2014 *)
PROG
(PARI) isok(n) = {if (n==1, return (0)); d = divisors(n); for (k=1, #d, if ((d[k] != 1) && (vecmax(digits(d[k])) != 9), return (0)); ); return (1); } \\ Michel Marcus, Nov 21 2015
(Magma) [n: n in [2..1000] | forall{Divisors(n)[i]: i in [2..NumberOfDivisors(n)] | 9 in Intseq(Divisors(n)[i])}]; // Bruno Berselli, Nov 21 2015
KEYWORD
base,easy,nonn
AUTHOR
Erich Friedman, Jul 04 2001
STATUS
approved