A062677 Numbers with property that every divisor (except 1) contains the digit 8.

83, 89, 181, 281, 283, 383, 389, 487, 587, 683, 787, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 983, 1087, 1181, 1187, 1283, 1289, 1381, 1481, 1483, 1487, 1489, 1583, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Comments

Subsequence of A011538, numbers with an 8. - Michel Marcus, Nov 21 2015

Examples

			7387 has divisors 83, 89 and 7387, all of which contain 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, A062678, A062679, A062680.

Programs

Maple

isA062677 := proc(n)
    if n = 1 then
        return false;
    end if;
    for d in numtheory[divisors](n) minus {1} do
        convert(convert(d,base,10),set) ;
        if  not 8 in % then
            return false;
        end if;
    end do:
    true ;
end proc:
for n from 1 to 2000 do
    if isA062677(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Mar 27 2017

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1900], fQ[#, 8] &] (* Robert G. Wilson v, Jun 11 2014 *)