login
Numbers with property that every divisor (except 1) contains the digit 8.
18

%I #25 Nov 07 2019 05:19:04

%S 83,89,181,281,283,383,389,487,587,683,787,809,811,821,823,827,829,

%T 839,853,857,859,863,877,881,883,887,983,1087,1181,1187,1283,1289,

%U 1381,1481,1483,1487,1489,1583,1783,1787,1789,1801,1811,1823,1831,1847,1861

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

%C Subsequence of A011538, numbers with an 8. - _Michel Marcus_, Nov 21 2015

%H Amiram Eldar, <a href="/A062677/b062677.txt">Table of n, a(n) for n = 1..10000</a>

%e 7387 has divisors 83, 89 and 7387, all of which contain the digit 8.

%p isA062677 := proc(n)

%p if n = 1 then

%p return false;

%p end if;

%p for d in numtheory[divisors](n) minus {1} do

%p convert(convert(d,base,10),set) ;

%p if not 8 in % then

%p return false;

%p end if;

%p end do:

%p true ;

%p end proc:

%p for n from 1 to 2000 do

%p if isA062677(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Mar 27 2017

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

%Y Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062678, A062679, A062680.

%K base,easy,nonn

%O 1,1

%A _Erich Friedman_, Jul 04 2001