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

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Comments

Different from A106093. 1691 = 19 * 89 is the smallest term that is not in A106093. - Franklin T. Adams-Watters, Apr 30 2007

Examples

			7961 has divisors 19, 419 and 7961, all of which contain the digit 9.
		

Links

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

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062680.

Programs

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

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 *)

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