A062678 Composite and every divisor (except 1) contains the digit 8.

6889, 7387, 23489, 25187, 31789, 32287, 34087, 48721, 50861, 56689, 60787, 68143, 68309, 68641, 68807, 73289, 73781, 76807, 78053, 78409, 78587, 78943, 78961, 80089, 81589, 87487, 88147, 98023, 98521, 106489, 106987, 108389, 110087

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			7387 has divisors 83, 89 and 7387, each of which contains the digit 8.
		

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, A062679, A062680.

Programs

Magma

[k:k in [2..120000]|  not IsPrime(k) and forall{d:d in Set(Divisors(k)) diff {1}| 8 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 110100], !PrimeQ[#] && fQ[#, 8] &] (* Robert G. Wilson v, Jun 11 2014 *)
dc8Q[n_]:=AllTrue[Rest[Divisors[n]],DigitCount[#,10,8]>0&]; Select[Range[ 111000],CompositeQ[ #]&&dc8Q[#]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2020 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019