A062679 Numbers such that every divisor (except 1, but including the number itself) contains the digit 9.

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

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

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.

Sequence in context: A379161 A092600 A106124 * A106093 A084666 A242265

Adjacent sequences: A062676 A062677 A062678 * A062680 A062681 A062682

Keyword

base,easy,nonn

Author

Erich Friedman, Jul 04 2001

Status

approved