|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
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
|
|
CROSSREFS
|
Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062680.
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|